Hirzebruch, Friedrich
Overview
Works:  238 works in 756 publications in 5 languages and 8,376 library holdings 

Genres:  Conference papers and proceedings Festschriften Biography History 
Roles:  Author, Editor, Honoree, Dedicatee, Other, Author of introduction, Contributor, Interviewee, Creator, Commentator 
Classifications:  QA564, 510 
Publication Timeline
.
Most widely held works about
Friedrich Hirzebruch
 The founders of index theory : reminiscences of and about Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I.M. Singer( Book )
 Das Glück, Mathematiker zu sein Friedrich Hirzebruch und seine Zeit by Winfried Scharlau( )
 Gesammelte Abhandlungen = Collected papers by Friedrich Hirzebruch( Book )
Most widely held works by
Friedrich Hirzebruch
Topological methods in algebraic geometry by
Friedrich Hirzebruch(
Book
)
51 editions published between 1966 and 2013 in 3 languages and held by 1,006 WorldCat member libraries worldwide
In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954
51 editions published between 1966 and 2013 in 3 languages and held by 1,006 WorldCat member libraries worldwide
In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954
Arbeitstagung Bonn, 1984 : proceedings of the meeting held by the MaxPlanckInstitut für Mathematik, Bonn, June 1522, 1984 by
Friedrich Hirzebruch(
Book
)
30 editions published between 1984 and 1985 in 3 languages and held by 560 WorldCat member libraries worldwide
To non commutative differential geometry  Special values of hecke Lfunctions and abelian integrals  An introduction to infinitesimal variations of hodge structures  New dimensions in geometry  Commentary on the article of manin  The mandelbrot set in a model for phase transitions  Recent developments in representation theory  Loop groups  Some recent results in complex manifold theory related to vanishing theorems for the semipositive case  Groups and group functors attached to kacmoody data  Modular points, modular curves, modular surfaces and modular forms  Eigenvalues of the dirac operator  Manifolds of non positive curvature  Metrics with holonomy G2 or spin (7)  On riemannian metrics adapted to threedimensional contact manifolds  4Manifolds with indefinite intersection form  Arithmetische Kompaktifizierung des Modulraums der abelschen Varietäten  The schottky problem  Vojta’s conjecture  A counterexample in 3space to a conjecture of H. Hopf  The topology and geometry of the moduli space of Riemann surfaces  Addendum
30 editions published between 1984 and 1985 in 3 languages and held by 560 WorldCat member libraries worldwide
To non commutative differential geometry  Special values of hecke Lfunctions and abelian integrals  An introduction to infinitesimal variations of hodge structures  New dimensions in geometry  Commentary on the article of manin  The mandelbrot set in a model for phase transitions  Recent developments in representation theory  Loop groups  Some recent results in complex manifold theory related to vanishing theorems for the semipositive case  Groups and group functors attached to kacmoody data  Modular points, modular curves, modular surfaces and modular forms  Eigenvalues of the dirac operator  Manifolds of non positive curvature  Metrics with holonomy G2 or spin (7)  On riemannian metrics adapted to threedimensional contact manifolds  4Manifolds with indefinite intersection form  Arithmetische Kompaktifizierung des Modulraums der abelschen Varietäten  The schottky problem  Vojta’s conjecture  A counterexample in 3space to a conjecture of H. Hopf  The topology and geometry of the moduli space of Riemann surfaces  Addendum
O(n)Mannigfaltigkeiten, exotische Sphären und Singularitäten by
Friedrich Hirzebruch(
Book
)
26 editions published between 1968 and 2007 in 4 languages and held by 550 WorldCat member libraries worldwide
GMannigfaltigkeiten  Spezielle GMannigfaltigkeiten  Der Klassifikationssatz für spezielle GMannigfaltigkeiten  Spezielle O(n)Mannigfaltigkeiten über D2  Die Mannigfaltigkeiten W2n?1(d)  Die Vielfachen des Tangentialbündels von Sn  Äquivariantes Verkleben  Die Homologie von Baummannigfaltigkeiten  Quadratische Formen, ARFsche Invariante  Bericht über Sphären  Sphären als Umgebungsränder von Singularitäten I  Die ganzzahlige homologie gewisser affin algebraischer Mannigfaltigkeiten  Ganzzahlige quadratische Formen  Sphären als Umgebungsränder von Singularitäten II  Periodische Abbildungen von Sphären
26 editions published between 1968 and 2007 in 4 languages and held by 550 WorldCat member libraries worldwide
GMannigfaltigkeiten  Spezielle GMannigfaltigkeiten  Der Klassifikationssatz für spezielle GMannigfaltigkeiten  Spezielle O(n)Mannigfaltigkeiten über D2  Die Mannigfaltigkeiten W2n?1(d)  Die Vielfachen des Tangentialbündels von Sn  Äquivariantes Verkleben  Die Homologie von Baummannigfaltigkeiten  Quadratische Formen, ARFsche Invariante  Bericht über Sphären  Sphären als Umgebungsränder von Singularitäten I  Die ganzzahlige homologie gewisser affin algebraischer Mannigfaltigkeiten  Ganzzahlige quadratische Formen  Sphären als Umgebungsränder von Singularitäten II  Periodische Abbildungen von Sphären
Prospects in mathematics by
Friedrich Hirzebruch(
Book
)
18 editions published between 1971 and 2010 in English and held by 514 WorldCat member libraries worldwide
18 editions published between 1971 and 2010 in English and held by 514 WorldCat member libraries worldwide
Neue topologische Methoden in der algebraischen Geometrie by
Friedrich Hirzebruch(
Book
)
26 editions published between 1955 and 1962 in 3 languages and held by 449 WorldCat member libraries worldwide
26 editions published between 1955 and 1962 in 3 languages and held by 449 WorldCat member libraries worldwide
Differentiable manifolds and quadratic forms by
Friedrich Hirzebruch(
Book
)
25 editions published between 1962 and 1992 in English and Undetermined and held by 417 WorldCat member libraries worldwide
25 editions published between 1962 and 1992 in English and Undetermined and held by 417 WorldCat member libraries worldwide
Lattices and codes : a course partially based on lectures by F. Hirzebruch by
Wolfgang Ebeling(
Book
)
11 editions published between 1994 and 2013 in English and German and held by 408 WorldCat member libraries worldwide
"The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the errorcorrecting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and errorcorrecting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory." "In the 2[superscript nd] edition numerous corrections and improvements have been made. More basic material has been included to make the text even more selfcontained. A new section on automorphism groups related to the Leech lattice has been added. Some hints to new results have been incorporated. Finally, several new exercises have been added."BOOK JACKET
11 editions published between 1994 and 2013 in English and German and held by 408 WorldCat member libraries worldwide
"The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the errorcorrecting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and errorcorrecting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory." "In the 2[superscript nd] edition numerous corrections and improvements have been made. More basic material has been included to make the text even more selfcontained. A new section on automorphism groups related to the Leech lattice has been added. Some hints to new results have been incorporated. Finally, several new exercises have been added."BOOK JACKET
Miscellanea mathematica by
Michael Francis Atiyah(
Book
)
14 editions published in 1991 in English and German and held by 343 WorldCat member libraries worldwide
Mathematics has a certain mystique, for it is pure and ex act, yet demands remarkable creativity. This reputation is reinforced by its characteristic abstraction and its own in dividual language, which often disguise its origins in and connections with the physical world. Publishing mathematics, therefore, requires special effort and talent. Heinz Gotze, who has dedicated his life to scientific pu blishing, took up this challenge with his typical enthusi asm. This Festschrift celebrates his invaluable contribu tions to the mathematical community, many of whose leading members he counts among his personal friends. The articles, written by mathematicians from around the world and coming from diverse fields, portray the important role of mathematics in our culture. Here, the reflections of important mathematicians, often focused on the history of mathematics, are collected, in recognition of Heinz Gotze's lifelong support of mathematics
14 editions published in 1991 in English and German and held by 343 WorldCat member libraries worldwide
Mathematics has a certain mystique, for it is pure and ex act, yet demands remarkable creativity. This reputation is reinforced by its characteristic abstraction and its own in dividual language, which often disguise its origins in and connections with the physical world. Publishing mathematics, therefore, requires special effort and talent. Heinz Gotze, who has dedicated his life to scientific pu blishing, took up this challenge with his typical enthusi asm. This Festschrift celebrates his invaluable contribu tions to the mathematical community, many of whose leading members he counts among his personal friends. The articles, written by mathematicians from around the world and coming from diverse fields, portray the important role of mathematics in our culture. Here, the reflections of important mathematicians, often focused on the history of mathematics, are collected, in recognition of Heinz Gotze's lifelong support of mathematics
The AtiyahSinger theorem and elementary number theory by
Friedrich Hirzebruch(
Book
)
13 editions published in 1974 in English and held by 335 WorldCat member libraries worldwide
13 editions published in 1974 in English and held by 335 WorldCat member libraries worldwide
Manifolds and modular forms by
Friedrich Hirzebruch(
Book
)
23 editions published between 1992 and 1994 in English and German and held by 325 WorldCat member libraries worldwide
During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the Agenus. The Agenus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the Agenus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the Agenus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold
23 editions published between 1992 and 1994 in English and German and held by 325 WorldCat member libraries worldwide
During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". I wanted to develop the theory of "Elliptic Genera" and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the Agenus. The Agenus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the Agenus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the Agenus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold
Algebraic geometry, Hirzebruch 70 : proceedings of the Algebraic Geometry Conference in honor of F. Hirzebruch's 70th birthday,
May 1116, 1998, Stefan Banach International Mathematical Center Warszawa, Poland by
Algebraic Geometry Conference in Honor of F. Hirzebruch's 70th Birthday(
Book
)
15 editions published between 1999 and 2012 in English and held by 274 WorldCat member libraries worldwide
15 editions published between 1999 and 2012 in English and held by 274 WorldCat member libraries worldwide
Arbeitstagung Bonn 2013 : in memory of Friedrich Hirzebruch by
Werner Ballmann(
)
4 editions published in 2016 in English and held by 264 WorldCat member libraries worldwide
This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 2228. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung. (4e de couv.)
4 editions published in 2016 in English and held by 264 WorldCat member libraries worldwide
This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 2228. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung. (4e de couv.)
Wolf prize in mathematics(
Book
)
8 editions published in 2001 in English and held by 228 WorldCat member libraries worldwide
The documents collected bibliographies, curricula vitae, autobiographical accounts, earlyimportant papers, lectures and speeches, as well as reports on the work of the prize winners by other. List of mathematicians concerned in this volume : Raoul Bott, A.P. Calderón, A.N. Kolmogorov, M.G. Krein, P.D. Dax, Hans Lewy, László Lovász, John W. Milnor, Jürgen L. Moser, Ilya PiatetskiShapiro, JeanPierre Serre, Carl L. Siegel, Yakov G. Sinai, Elias M. Stein, Jacques Tits, André Weil, Hassler Whitney, Andrew J. Wiles, Oscae Zariski
8 editions published in 2001 in English and held by 228 WorldCat member libraries worldwide
The documents collected bibliographies, curricula vitae, autobiographical accounts, earlyimportant papers, lectures and speeches, as well as reports on the work of the prize winners by other. List of mathematicians concerned in this volume : Raoul Bott, A.P. Calderón, A.N. Kolmogorov, M.G. Krein, P.D. Dax, Hans Lewy, László Lovász, John W. Milnor, Jürgen L. Moser, Ilya PiatetskiShapiro, JeanPierre Serre, Carl L. Siegel, Yakov G. Sinai, Elias M. Stein, Jacques Tits, André Weil, Hassler Whitney, Andrew J. Wiles, Oscae Zariski
Gesammelte Abhandlungen = Collected papers by
Friedrich Hirzebruch(
Book
)
28 editions published between 1987 and 2018 in 4 languages and held by 214 WorldCat member libraries worldwide
28 editions published between 1987 and 2018 in 4 languages and held by 214 WorldCat member libraries worldwide
Surveys in differential geometry : papers dedicated to Atiyah, Bott, Hirzebruch, and Singer by Conference on Geometry and Topology(
Book
)
13 editions published between 2000 and 2002 in English and held by 206 WorldCat member libraries worldwide
13 editions published between 2000 and 2002 in English and held by 206 WorldCat member libraries worldwide
Lectures on Hilbert modular surfaces by
Friedrich Hirzebruch(
Book
)
10 editions published in 1981 in English and held by 187 WorldCat member libraries worldwide
10 editions published in 1981 in English and held by 187 WorldCat member libraries worldwide
Einführung in die Funktionalanalysis by
Friedrich Hirzebruch(
Book
)
24 editions published between 1971 and 2009 in German and Undetermined and held by 183 WorldCat member libraries worldwide
24 editions published between 1971 and 2009 in German and Undetermined and held by 183 WorldCat member libraries worldwide
Zur algebraischen Geometrie : selected papers by
B. L. van der Waerden(
Book
)
8 editions published between 1973 and 2013 in German and English and held by 166 WorldCat member libraries worldwide
8 editions published between 1973 and 2013 in German and English and held by 166 WorldCat member libraries worldwide
Geradenkonfigurationen und algebraische Flächen by
Gottfried Barthel(
Book
)
11 editions published between 1987 and 1990 in German and held by 150 WorldCat member libraries worldwide
11 editions published between 1987 and 1990 in German and held by 150 WorldCat member libraries worldwide
Hilbert modular surfaces by
Friedrich Hirzebruch(
Book
)
6 editions published between 1972 and 1973 in English and held by 120 WorldCat member libraries worldwide
6 editions published between 1972 and 1973 in English and held by 120 WorldCat member libraries worldwide
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Related Identities
 Atiyah, Michael Francis 1929 Honoree Author Dedicatee
 Mayer, K. H.
 Suter, S. (Silke) 1943 Other Editor
 Schwermer, Joachim Other Editor
 Zagier, Don 1951 Editor
 Ebeling, Wolfgang Author
 Koh, S. S.
 Remmert, Reinhold Editor
 Neumann, W. D. (Walter David) 1946
 Singer, I. M. (Isadore Manuel) 1924 Honoree Dedicatee
Useful Links
Associated Subjects
Algebra Algebraic topology Atiyah, Michael Francis, Bott, Raoul, Coding theory Differentiable manifolds Differential topology Discontinuous groups Einstein manifolds Engineering Finite fields (Algebra) Fixed point theory Forms, Modular Forms, Quadratic Functional analysis Geometry Geometry, Algebraic Geometry, Differential Germany Global analysis (Mathematics) Group theory Hilbert modular surfaces Hilbert space Hirzebruch, Friedrich History Homology theory Index theory (Mathematics) Lattice theory Lie algebras Manifolds (Mathematics) Mathematicians Mathematics Modular groups Number theory Operator theory Singer, I. M.(Isadore Manuel), Singularities (Mathematics) Sphere Surfaces, Algebraic Topology Wolf Foundation Prizes
Covers
Alternative Names
Chircebruch, F.
Chircebruch, F. 19272012
Chircebruch, F. [t]
Friedrich Ernst Peter Hirzebruch.
Friedrich Hirzebruch deutscher Mathematiker
Friedrich Hirzebruch Duits wiskundige
Friedrich Hirzebruch German mathematician
Friedrich Hirzebruch matemàtic alemany
Friedrich Hirzebruch matemático alemán
Friedrich Hirzebruch matematico tedesco
Friedrich Hirzebruch mathématicien allemand
Friedrich Hirzebruch tysk matematikar
Friedrich Hirzebruch tysk matematiker
Hircebruh, F.
Hirzebruch F.
Hirzebruch, F. 19272012
Hirzebruch, F. (Friedrich)
Hirzebruch, Friedrch E.P. 1927
Hirzebruch, Friedrich.
Hirzebruch, Friedrich E. 19272012
Hirzebruch, Friedrich E. P. 19272012
Hirzebruch, Friedrich Ernst Peter.
Hirzebruch, Friedrich Ernst Peter 1927...
Hirzebruch Friedrich Ernst Peter 19272012
Hirzebruch, Fritz
Hirzebruch, Fritz 1927
Hirzebruch, Fritz 19272012
Фридрих Хирцебрух
Хирцебрух Ф.
Хирцебрух, Фридрих
فريدريش هيرتسبروخ رياضياتي ألماني
프리드리히 히르체브루흐
ヒルツェブルフ
フリードリッヒ・ヒルツェブルフ ドイツの数学者
弗里德里希·希策布鲁赫
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