20 citations · 68 across the 17 of their papers we have counts for
18 papers
Reflective lattices and hyperkahler manifolds
Ekaterina Amerik, Andrey Soldatenkov, Misha Verbitsky
Using the results of Nikulin and Vinberg on the groups of isometries generated by reflections, we construct a subvariety called the Nikulin-Vinberg locus in the moduli space of pol…
Birational geometry of hyperkahler manifolds and the Hu-Yau conjecture
Ekaterina Amerik, Andrey Soldatenkov, Misha Verbitsky
Wierzba and Wisniewski proved that in dimension 4, every bimeromorphic map of hyperkahler manifolds is represented as a composition of Mukai flops. Hu and Yau conjectured that this…
The abundance and SYZ conjectures in families of hyperkahler manifolds
Andrey Soldatenkov, Misha Verbitsky
Let be a holomorphic line bundle on a hyperkahler manifold , with nef and not big. SYZ conjecture predicts that is semiample. We prove that this is true, assumi…
Hermitian-symplectic and Kahler structures on degenerate twistor deformations
Andrey Soldatenkov, Misha Verbitsky
Let be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration , and a closed -form on . Then is a holo…
Apollonian carpets and the boundary of the Kahler cone of a hyperkahler manifold
Ekaterina Amerik, Andrey Soldatenkov, Misha Verbitsky
The ample cone of a compact Kahler -manifold is the intersection of its Kahler cone and the real subspace generated by integer (1,1)-classes. Its isotropic boundary is the s…
Rigid currents on compact hyperkahler manifolds
Nessim Sibony, Andrey Soldatenkov, Misha Verbitsky
A rigid cohomology class on a complex manifold is a class that is represented by a unique closed positive current. The positive current representing a rigid class is also called ri…
Cohomology and André motives of hyperkähler orbifolds
Andrey Soldatenkov
One of the main tools for the study of compact hyperkähler manifolds is the natural action of the Looijenga-Lunts-Verbitsky Lie algebra on the cohomology of such manifolds. This al…
The Moser isotopy for holomorphic symplectic and C-symplectic structures
Andrey Soldatenkov, Misha Verbitsky
A C-symplectic structure is a complex-valued 2-form which is holomorphically symplectic for an appropriate complex structure. We prove an analogue of Moser's isotopy theorem for fa…
On the Hodge structures of compact hyperkähler manifolds
Andrey Soldatenkov
The purpose of this note is to give an account of a well-known folklore result: the Hodge structure on the second cohomology of a compact hyperkähler manifold uniquely determines H…
Deformation principle and André motives of projective hyperkähler manifolds
Andrey Soldatenkov
Let and be deformation equivalent projective hyperkähler manifolds. We prove that the André motive of is abelian if and only if the André motive of is abeli…
Limit mixed Hodge structures of hyperkähler manifolds
Andrey Soldatenkov
This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk…
The Kuga-Satake construction under degeneration
Stefan Schreieder, Andrey Soldatenkov
We extend the Kuga-Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga-Satake ab…
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…
On the geometry of the LLSvS eightfold
Evgeny Shinder, Andrey Soldatenkov
In this note we make a few remarks about the geometry of the holomorphic symplectic manifold Z constructed by C.Lehn, M.Lehn, C.Sorger and D. van Straten as a two-step contraction…
k-symplectic structures and absolutely trianalytic subvarieties in hyperkahler manifolds
Andrey Soldatenkov, Misha Verbitsky
Let be a hyperkahler manifold, and a complex subvariety in . We say that is trianalytic if it is complex analytic with respect to and $K…
Holomorphic Lagrangian fibrations on hypercomplex manifolds
Andrey Soldatenkov, Misha Verbitsky
A hypercomplex manifold is a manifold equipped with a triple of complex structures satisfying the quaternionic relations. A holomorphic Lagrangian variety on a hypercomplex manifol…
Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)
Andrey Soldatenkov, Misha Verbitsky
A hypercomplex manifold M is a manifold with a triple I,J,K of complex structure operators satisfying quaternionic relations. For each quaternion L=aI +bJ+cK, L^2=-1, L is also a c…
Holonomy of the Obata connection on SU(3)
Andrey Soldatenkov
A hypercomplex structure on a smooth manifold is a triple of integrable almost complex structures satisfying quaternionic relations. The Obata connection is the unique torsion-free…