78 citations · 295 across the 35 of their papers we have counts for
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On the classification of hyperbolic root systems of the rank three. Part II
Viacheslav V. Nikulin
Here we prove classification results announced in Part I (alg-geom/9711032). We classify maximal hyperbolic root systems of the rank 3 having restricted arithmetic type and a gener…
On the classification of hyperbolic root systems of the rank three. Part I
Viacheslav V. Nikulin
It was recently understood that from the point of view of automorphic Lorentzian Kac-Moody algebras and some aspects of Mirror Symmetry, interesting hyperbolic root systems should…
K3 surfaces with interesting groups of automorphisms
Viacheslav V. Nikulin
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 lattice S_X are…
Automorphic Forms and Lorentzian Kac-Moody Algebras. Part II
Valeri A. Gritsenko, Viacheslav V. Nikulin
We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular group…
Automorphic Forms and Lorentzian Kac--Moody Algebras. Part I
Valeri A. Gritsenko, Viacheslav V. Nikulin
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 t…
The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras
Valeri A. Gritsenko, Viacheslav V. Nikulin
We find automorphic corrections for the Lorentzian Kac--Moody algebras with the simplest generalized Cartan matrices of rank 3: A_{1,0} = 2 0 -1 0 2 -2 -1 -2 2 and A_{1,I} = 2 -2 -…
The Remark on Discriminants of K3 Surfaces Moduli as Sets of Zeros of Automorphic Forms
Viacheslav V. Nikulin
We show that for any there exists a natural even such that the discriminant of moduli of K3 surfaces of the degree is not equal to the set of zeros of any automorph…
K3 surfaces, Lorentzian Kac--Moody algebras and Mirror Symmetry
Valeri A. Gritsenko, Viacheslav V. Nikulin
We consider the variant of Mirror Symmetry Conjecture for K3 surfaces which relates "geometry" of curves of a general member of a family of K3 with "algebraic functions" on the mod…
Siegel automorphic form corrections of some Lorentzian Kac--Moody Lie algebras
Valeri A. Gritsenko, Viacheslav V. Nikulin
We find automorphic form corrections which are generalized Lorentzian Kac--Moody superalgebras without odd real simple roots (see R. Borcherds \cite{Bo1} -- \cite{Bo7}, V. Kac \cit…
Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras
Viacheslav V. Nikulin
This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature ) integral symmetric bilinear for…
A lecture on Kac--Moody Lie algebras of the arithmetic type
Viacheslav V. Nikulin
We name an indecomposable symmetrizable generalized Cartan matrix and the corresponding Kac--Moody Lie algebra ${\goth g} ^\prime (A)$ {\it of the arithmetic type} if for any $…
Algebraic Surfaces with Log-Terminal Singularities and nef Anticanonical Class and Reflection Groups in Lobachevsky Spaces. I (Basics of the Diagram Method)
Viacheslav V. Nikulin
In our preprint: "Algebraic surfaces with log-terminal singularities and nef anticanonical class and reflection groups in Lobachevsky spaces", Preprint Max-Planck-Institut für Math…
Diagram Method for 3-Folds and its Application to Kahler Cone and Picard Number of Calabi-Yau 3-Folds, I. with Appendix by Vyacheslav V. Shokurov: "Anticanonical boundedness for curves"
Viacheslav V. Nikulin
We prove the general diagram method theorem valid for the quite large class of 3-folds with Q-factorial singularities (see Basic Theorem 1.3.2 and also Theorem 2.2.6). This gives t…
On the Topological Classification of Real Enriques Surfaces. I
Viacheslav V. Nikulin
This note contains preliminary calculation of topological types or real Enriques surfaces. We realize 59 topological types of real Enriques surfaces (Theorem 6) and show that all o…
On the Brauer Group of Real Algebraic Surfaces
Viacheslav V. Nikulin
Let X be a real projective algebraic manifold, s numerates connected components of X(R) and _2Br(X) the subgroup of elements of order 2 of the cohomological Brauer group Br(X). We…
On Brauer Groups of Real Enriques Surfaces
V. V. Nikulin, R. Sujatha
Let Y be a real Enriques surface, _2Br(Y) the subgroup of elements of order 2 of Br(Y), and s, s_{or}, and s_{nor} the number of all connected, connected orientable, and connected…
On the Picard Number of Fano 3-Folds with Terminal Singularities
Viacheslav V. Nikulin
We prove the following main result: Let X be a Fano 3-fold with terminal Q-factorial singularities and X does not have a small extremal ray and a face of Kodaira dimension 1 or 2 f…