WorldCat Identities

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
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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 non-Euclidean 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 Cohn-Vossen'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

Del Pezzo and K3 surfaces by Valery Alexeev( Book )

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

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

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

Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac-Moody lie algebras by V. V Nikulin( Book )

4 editions published in 1995 in English and German and held by 6 WorldCat member libraries worldwide

Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras by Valerij A Gricenko( Book )

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

Kikagaku to gun( Book )

2 editions published in 1993 in Japanese and held by 4 WorldCat member libraries worldwide

The arithmetic mirror symmetry and Calabi-Yau 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 Calabi-Yau 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 Calabi-Yau manifolds. Recently there were several papers by physicists where it was shown on some examples. We propose a problem of classification of introduced Calabi-Yau 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 Calabi-Yau 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

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

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. Piatetsky-Shapiro 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 non-trivial 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 Kac-Moody algebras and Mirror Symmetry."
Algebraic 3-folds 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

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 V-arithmetic 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 Kac-Moody algebras by Valery A Gritsenko( Book )

1 edition published in 2002 in English and held by 2 WorldCat member libraries worldwide

The igusa modular forms and "the simplest" Lorentzian Kac-Moody algebras by Valeri A Gritsenko( Book )

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

Algebraic surfaces with log-terminal 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

 
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Audience level: 0.60 (from 0.54 for Geometries ... to 0.95 for O klassifi ...)

Geometries and groups
Covers
Del Pezzo and K3 surfaces
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.

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