78 citations · 213 across the 15 of their papers we have counts for
9 papers · 1 filter
Commutator coverings of Siegel threefolds
V. Gritsenko, K. Hulek
We investigate the existence and non-existence of modular forms of low weight with a character with respect to the paramodular group and discuss the resulting geometric conse…
A lecture on Arithmetic Mirror Symmetry and Calabi-Yau manifolds
Valeri A. Gritsenko, Viacheslav V. Nikulin
We extend our variant of mirror symmetry for K3 surfaces \cite{GN3} and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models…
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 -…
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…