14 citations · 28 across the 9 of their papers we have counts for
9 papers · 1 filter
Geometry and automorphisms of non-Kähler holomorphic symplectic manifolds
Fedor Bogomolov, Nikon Kurnosov, Alexandra Kuznetsova +1
We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works of D. Guan and the first author. Any such manifold of di…
Deformations and BBF form on non-Kahler holomorphically symplectic manifolds
Nikon Kurnosov, Misha Verbitsky
In 1995, Dan Guan constructed examples of non-Kahler, simply-connected holomorphically symplectic manifolds. An alternative construction, using the Hilbert scheme of Kodaira-Thurst…
Lagrangian fibrations for IHS fourfolds
Fedor Bogomolov, Nikon Kurnosov
In this paper we study the Lagrangian fibrations for projective irreducible symplectic fourfolds and exclude the case of non-smooth base. Our method could be extended to the higher…
Automorphisms of hyperkähler manifolds and groups acting on CAT(0) spaces
Nikon Kurnosov, Egor Yasinsky
We study groups of bimeromorphic and biholomorphic automorphisms of projective hyperkähler manifolds. Using an action of these groups on some non-positively curved space, we deduce…
Classifying surfaces with via group theory
Federico Buonerba, Fedor Bogomolov, Nikon Kurnosov
We give a new proof of a theorem of Bogomolov, that the only surfaces with are those constructed by Hopf and Inoue. The proof follows the strategy of the original…
Kuga-Satake construction and cohomology of hyperkahler manifolds
Nikon Kurnosov, Andrey Soldatenkov, Misha Verbitsky
Let M be a simple hyperkahler manifold. Kuga-Satake construction gives an embedding of H^2(M,C) into the second cohomology of a torus, compatible with the Hodge structure. We const…
Boundness of for hyperkähler manifolds with vanishing odd-Betti numbers
Nikon Kurnosov
We prove that is bounded for hyperkähler manifolds with vanishing odd-Betti numbers. The explicit upper boundary is conjectured. Following the method described by Sawon we pr…
Absolutely trianalytic tori in the generalized Kummer variety
Nikon Kurnosov
We prove that a generic complex deformation of a generalized Kummer variety contains no complex analytic tori.
The second Betti number of hyperkähler manifolds
Nikon Kurnosov
Let be a compact irreducible hyperkahler manifold, from Bogomolov inequality [V1] we obtain forbidden values of the second Betti number in arbitrary dimension. UPD: Unfor…