Никулин, В. В (Вячеслав Валентинович)
Overview
Works:  46 works in 113 publications in 4 languages and 970 library holdings 

Genres:  History 
Roles:  Author 
Classifications:  QA445, 516 
Publication Timeline
.
Most widely held works by
В. В Никулин
Geometries and groups by
V. V Nikulin(
Book
)
31 editions published between 1983 and 1994 in English and Russian and held by 676 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."
31 editions published between 1983 and 1994 in English and Russian and held by 676 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
)
2 editions published in 2000 in English and held by 64 WorldCat member libraries worldwide
2 editions published in 2000 in English and held by 64 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 14 WorldCat member libraries worldwide
1 edition published in 2001 in Russian and held by 14 WorldCat member libraries worldwide
On the classification of hyperbolic root systems of rank three by
V. V Nikulin(
Book
)
8 editions published in 2000 in English and held by 14 WorldCat member libraries worldwide
8 editions published in 2000 in English and held by 14 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
)
3 editions published in 1995 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 5 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
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
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
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."
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 surfaces with logterminal singularities and nef anticanonical class and reflection groups in Lobachevsky spaces by
V. V Nikulin(
Book
)
2 editions published in 1989 in German and English and held by 3 WorldCat member libraries worldwide
2 editions published in 1989 in German and English and held by 3 WorldCat member libraries worldwide
On rational maps between K3 surfaces by
V. V Nikulin(
Book
)
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
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
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
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
Weil linear systems on singular K3 surfaces by
V. V Nikulin(
Book
)
2 editions published in 1990 in German and English and held by 2 WorldCat member libraries worldwide
2 editions published in 1990 in German and English and held by 2 WorldCat member libraries worldwide
Automorphic forms and Lorentzian KacMoody algebras by V. A Gritzenko(
Book
)
2 editions published in 1996 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Using the general method which was applied to prove finiteness of the set of hyperbolic generalized Cartan matrices of elliptic and parabolic type, we classify all symmetric (and twisted to symmetric) hyperbolic generalized Cartan matrices of elliptic type and of rank 3 with a lattice Weyl vector. We develop the general theory of reflective lattices T with 2 negative squares and reflective automorphic forms on homogenous domains of type IV defined by T. We consider this theory as mirror symmetric to the theory of elliptic and parabolic hyperbolic reflection groups and corresponding hyperbolic root systems. We formulate Arithmetc Mirror Symmetry Conjecture relating both these theories and prove some statements to support this Conjecture. This subject is connected with automorphic correction of Lorentzian KacMoody algebras. We define Lie reflective automorphic forms which are the most beautiful automorphic forms defining automorphic Lorentzian KacMoody algebras and formulate finiteness Conjecture for these forms. Detailed study of automorphic correction and Lie reflective automorphic forms for generalized Cartan matrices mentioned above will be given in Part II."
2 editions published in 1996 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Using the general method which was applied to prove finiteness of the set of hyperbolic generalized Cartan matrices of elliptic and parabolic type, we classify all symmetric (and twisted to symmetric) hyperbolic generalized Cartan matrices of elliptic type and of rank 3 with a lattice Weyl vector. We develop the general theory of reflective lattices T with 2 negative squares and reflective automorphic forms on homogenous domains of type IV defined by T. We consider this theory as mirror symmetric to the theory of elliptic and parabolic hyperbolic reflection groups and corresponding hyperbolic root systems. We formulate Arithmetc Mirror Symmetry Conjecture relating both these theories and prove some statements to support this Conjecture. This subject is connected with automorphic correction of Lorentzian KacMoody algebras. We define Lie reflective automorphic forms which are the most beautiful automorphic forms defining automorphic Lorentzian KacMoody algebras and formulate finiteness Conjecture for these forms. Detailed study of automorphic correction and Lie reflective automorphic forms for generalized Cartan matrices mentioned above will be given in Part II."
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
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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
 Vsesoi︠u︡znyĭ institut nauchnoĭ i tekhnicheskoĭ informat︠s︡ii (Soviet Union)
 Gritsenko, Valery A. Author
 Gritzenko, Valeri A. Author
 Mathematical Sciences Research Institute (Berkeley, Calif.)
 Saito, Sachiko
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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 Topology UkraineChornobylʹ
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
Никулин, В. В. (Вячеслав Валентинович)
Никулин, Вячеслав Валентинович.
ニクリン, V. V.
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