Никулин, В. В (Вячеслав Валентинович)
Overview
Works:  55 works in 121 publications in 4 languages and 975 library holdings 

Genres:  History 
Roles:  Author 
Publication Timeline
.
Most widely held works by
В. В Никулин
Geometries and groups by
V. V Nikulin(
Book
)
30 editions published between 1983 and 1994 in English and held by 705 WorldCat member libraries worldwide
This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's nonEuclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and CohnVossen's "Geometry and the imagination" and Weyl's "Symmetry."
30 editions published between 1983 and 1994 in English and held by 705 WorldCat member libraries worldwide
This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's nonEuclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and CohnVossen's "Geometry and the imagination" and Weyl's "Symmetry."
On the classification of hyperbolic root systems of rank three by
V. V Nikulin(
Book
)
10 editions published in 2000 in English and held by 79 WorldCat member libraries worldwide
10 editions published in 2000 in English and held by 79 WorldCat member libraries worldwide
Del Pezzo and K3 surfaces by
Valery Alexeev(
Book
)
7 editions published in 2006 in English and held by 61 WorldCat member libraries worldwide
7 editions published in 2006 in English and held by 61 WorldCat member libraries worldwide
Geometrii i gruppy by
V. V Nikulin(
Book
)
4 editions published in 1983 in Russian and held by 25 WorldCat member libraries worldwide
4 editions published in 1983 in Russian and held by 25 WorldCat member libraries worldwide
My oshchushchali zapakh bedy : ot Kovrova do Chernobyli︠a︡ : trevogi, nadezhdy, povoroty sudʹby v atomnom veke(
Book
)
1 edition published in 2001 in Russian and held by 15 WorldCat member libraries worldwide
1 edition published in 2001 in Russian and held by 15 WorldCat member libraries worldwide
O klassifikacii giperboličeskich sistem kornej ranga tri by
V. V Nikulin(
Book
)
3 editions published in 2000 in Russian and held by 7 WorldCat member libraries worldwide
3 editions published in 2000 in Russian and held by 7 WorldCat member libraries worldwide
Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian KacMoody lie algebras by
V. V Nikulin(
Book
)
4 editions published in 1995 in English and German and held by 6 WorldCat member libraries worldwide
4 editions published in 1995 in English and German and held by 6 WorldCat member libraries worldwide
Siegel automorphic form corrections of some Lorentzian KacMoody Lie algebras by
Valerij A Gricenko(
Book
)
2 editions published in 1995 in German and English and held by 5 WorldCat member libraries worldwide
2 editions published in 1995 in German and English and held by 5 WorldCat member libraries worldwide
O klassifikat︠s︡ii giperbolicheskikh sistem korneĭ ranga tri by
V. V Nikulin(
Book
)
1 edition published in 2000 in Russian and held by 4 WorldCat member libraries worldwide
1 edition published in 2000 in Russian and held by 4 WorldCat member libraries worldwide
Kikagaku to gun(
Book
)
2 editions published in 1993 in Japanese and held by 4 WorldCat member libraries worldwide
2 editions published in 1993 in Japanese and held by 4 WorldCat member libraries worldwide
The arithmetic mirror symmetry and CalabiYau manifolds by
V. A Gritsenko(
Book
)
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We extend our variant of mirror symmetry for K3 surfaces [GN3] and clarify its relation with mirror symmetry for CalabiYau manifolds. We introduce two classes (for the models A and B) of Calabi Yau manifolds fibrated by K3 surfaces with some special Picard lattices. These two classes are related with automorphic forms on IV type domains which we studied in our papers [GN1][GN6]. Conjecturally these automorphic forms take part in the quantum intersection pairing for model A, Yukawa coupling for model B and mirror symmetry between these two classes of CalabiYau manifolds. Recently there were several papers by physicists where it was shown on some examples. We propose a problem of classification of introduced CalabiYau manifolds. Our papers [GN1][GN6] and [N3][N14] give a hope that this is possible. They describe possible Picard or transcendental lattices of general K3 fibers of the CalabiYau manifolds."
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We extend our variant of mirror symmetry for K3 surfaces [GN3] and clarify its relation with mirror symmetry for CalabiYau manifolds. We introduce two classes (for the models A and B) of Calabi Yau manifolds fibrated by K3 surfaces with some special Picard lattices. These two classes are related with automorphic forms on IV type domains which we studied in our papers [GN1][GN6]. Conjecturally these automorphic forms take part in the quantum intersection pairing for model A, Yukawa coupling for model B and mirror symmetry between these two classes of CalabiYau manifolds. Recently there were several papers by physicists where it was shown on some examples. We propose a problem of classification of introduced CalabiYau manifolds. Our papers [GN1][GN6] and [N3][N14] give a hope that this is possible. They describe possible Picard or transcendental lattices of general K3 fibers of the CalabiYau manifolds."
On rational maps between K3 surfaces by
V. V Nikulin(
Book
)
3 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide
On the topological classification of real Enriques surfaces by
V. V Nikulin(
Book
)
2 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
K3 surfaces with interesting groups of automorphisms by
V. V Nikulin(
Book
)
2 editions published in 1997 in English and held by 3 WorldCat member libraries worldwide
Abstract: "By the fundamental result of I.I. PiatetskyShapiro and I.R. Shafarevich (1971), the automorphism group Aut(X) of a K3 surface X over C and its action on the Picard lattices S[subscript X] are prescribed by the Picard lattice S[subscript X]. We use this result and our method (1980) to show finiteness of the set of Picard lattices S[subscript X] of rank [> or =] 3 such that the automorphism group Aut(X) of the K3 surface X has a nontrivial invariant sublattice S₀ in S[subscript X] where the group Aut(X) acts as a finite group. For hyperbolic and parabolic lattices S₀ it has been proved by the author before (1980, 1995). Thus we extend this results to negative sublattices S₀. We give several examples of Picard lattices S[subscript X] with parabolic and negative S₀. We also formulate the corresponding finiteness result for reflective hyperbolic lattices of hyperbolic type over purely real algebraic number fields. These results are important for the theory of Lorentzian KacMoody algebras and Mirror Symmetry."
2 editions published in 1997 in English and held by 3 WorldCat member libraries worldwide
Abstract: "By the fundamental result of I.I. PiatetskyShapiro and I.R. Shafarevich (1971), the automorphism group Aut(X) of a K3 surface X over C and its action on the Picard lattices S[subscript X] are prescribed by the Picard lattice S[subscript X]. We use this result and our method (1980) to show finiteness of the set of Picard lattices S[subscript X] of rank [> or =] 3 such that the automorphism group Aut(X) of the K3 surface X has a nontrivial invariant sublattice S₀ in S[subscript X] where the group Aut(X) acts as a finite group. For hyperbolic and parabolic lattices S₀ it has been proved by the author before (1980, 1995). Thus we extend this results to negative sublattices S₀. We give several examples of Picard lattices S[subscript X] with parabolic and negative S₀. We also formulate the corresponding finiteness result for reflective hyperbolic lattices of hyperbolic type over purely real algebraic number fields. These results are important for the theory of Lorentzian KacMoody algebras and Mirror Symmetry."
Algebraic 3folds and diagram method by
V. V Nikulin(
Book
)
3 editions published in 1990 in English and German and held by 3 WorldCat member libraries worldwide
3 editions published in 1990 in English and German and held by 3 WorldCat member libraries worldwide
The transition constant for arithmetic hyperbolic reflection groups by
V. V Nikulin(
)
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
The transition constant was introduced in our 1981 paper and denoted as N(14). It is equal to the maximal degree of the ground fields of Varithmetic connected edge graphs with 4 vertices and of the minimality 14. This constant is fundamental since if the degree of the ground field of an arithmetic hyperbolic reflection group is greater than N(14), then the field comes from special plane reflection groups. In [14], we claimed its upper bound 56. Using similar but more di±cult considerations, here we show that the upper bound is 25. As applications, using this result and our methods, we show that the degree of ground fields of arithmetic hyperbolic reflection groups in dimensions at least 6 has the upper bound 25; in dimensions 3; 4; 5 it has the upper bound 44. This significantly improves our results in [14, 15, 16]. Additionally using recent results by Belolipetsky and Maclachlan, the last upper bound can be improved to 35. In Appendix, we give a review and corrections to Section 1 of our papers [10] which is important for our methods
1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide
The transition constant was introduced in our 1981 paper and denoted as N(14). It is equal to the maximal degree of the ground fields of Varithmetic connected edge graphs with 4 vertices and of the minimality 14. This constant is fundamental since if the degree of the ground field of an arithmetic hyperbolic reflection group is greater than N(14), then the field comes from special plane reflection groups. In [14], we claimed its upper bound 56. Using similar but more di±cult considerations, here we show that the upper bound is 25. As applications, using this result and our methods, we show that the degree of ground fields of arithmetic hyperbolic reflection groups in dimensions at least 6 has the upper bound 25; in dimensions 3; 4; 5 it has the upper bound 44. This significantly improves our results in [14, 15, 16]. Additionally using recent results by Belolipetsky and Maclachlan, the last upper bound can be improved to 35. In Appendix, we give a review and corrections to Section 1 of our papers [10] which is important for our methods
On classification of Lorentzian KacMoody algebras by Valery A Gritsenko(
Book
)
1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide
The igusa modular forms and "the simplest" Lorentzian KacMoody algebras by
Valeri A Gritsenko(
Book
)
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
Classification of log del Pezzo surfaces of index ≤ 2 by
Valery Alexeev(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
Algebraic surfaces with logterminal singularities and nef anticanonical class and reflection groups in Lobachevsky spaces by
V. V Nikulin(
Book
)
1 edition published in 1989 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 1989 in German and held by 2 WorldCat member libraries worldwide
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Related Identities
 Шафаревич, И. Р (Игорь Ростиславович) 1923
 Alexeev, Valery 1964 Author
 Reid, Miles Translator
 Gritsenko, Valeri A. Author
 根上, 生也 1957
 MaxPlanckInstitut für Mathematik (Bonn)
 Vsesoi︠u︡znyĭ institut nauchnoĭ i tekhnicheskoĭ informat︠s︡ii (Soviet Union)
 Gritsenko, Valery A. Author
 Sonderforschungsbereich 170Geometrie und Analysis
 Mathematical Sciences Research Institute (Berkeley, Calif.)
Useful Links
Associated Subjects
Automorphic functions Chernobyl Nuclear Accident (Chornobylʹ, Ukraine : Geometry Group theory Group theoryReflections Hyperbolic groups Hyperbolic spaces KacMoody algebras Lattice theory Lie algebras Mathematics Mirror symmetry Root systems (Algebra) Russia (Federation)Kovrov Surfaces, Algebraic Topology UkraineChornobylʹ
Covers
Alternative Names
Nikouline Viatcheslav Valentinovitch
Nikulin, V. V.
Nikulin, Viacheslav V.
Nikulin Viacheslav Valentinovich
Nikulin, Vjačeslav Valentinovič
Nikulin, Vjačeslav Valentinovič. [t]
Viacheslav V. Nikulin matemático ruso
Viacheslav V. Nikulin Russian mathematician
Вячеслав Валентинович Никулин российский математик
Никулин, В. В. (Вячеслав Валентинович)
Никулин, Вячеслав Валентинович.
ニクリン, V. V.
Languages