25 citations · 76 across the 23 of their papers we have counts for
26 papers
Lagrangian fibrations on hyperkahler manifolds have no multiple fibers in codimension one
Ljudmila Kamenova, Misha Verbitsky
Let be a Lagrangian fibration on a compact hyperkahler manifold. We prove that has no multiple fibers in codimension 1. We prove that this condition…
Correspondences for hyperkähler varieties with large Picard numbers
Ljudmila Kamenova, Abhinav Kumar
In this note, we explore the connection between hyperkähler manifolds with large Picard numbers and abelian varieties. In particular, we are interested in Morrison's solution to th…
Minimal multiplicity of fiber components in abelian fibrations
Frederic Campana, Ljudmila Kamenova, Misha Verbitsky
An abelian fibration is a proper projective surjective map of complex varieties with general fiber an abelian variety. Consider a multiple fiber of an abelian fibration, and let $m…
On anti-hyperbolicity for hyperkähler varieties
Ljudmila Kamenova, Steven Lu
By restricting to (a linear subspace of) an affine chart in projective space, a complex stably rational or unirational manifold of dimension is meromorphically dominable by $\m…
Torsor Neron models of hyperkahler manifolds
Ljudmila Kamenova, Misha Verbitsky
Let be a compact hyperkahler manifold equipped with a Lagrangian fibration , and the smooth locus of . We prove that over a complement to a codimension $\…
Sections of Lagrangian fibrations on holomorphic symplectic manifolds
Fedor Bogomolov, Ljudmila Kamenova, Misha Verbitsky
Let be a holomorphically symplectic manifold, equipped with a Lagrangian fibration . A degenerate twistor deformation (sometimes also called ``a Tate-Shafarevich…
Some density results for hyperkähler manifolds
Yajnaseni Dutta, Elham Izadi, Ljudmila Kamenova +1
Lagrangian fibrations of hyperkähler manifolds are induced by semi-ample line bundles which are isotropic with respect to the Beauville-Bogomolov-Fujiki form. For a non-isotrivial…
Finiteness of stable Lagrangian fibrations
Ljudmila Kamenova
In this paper we survey some finiteness results of the deformation classes of hyperkähler Lagrangian fibrations, and we prove finiteness for stable Lagrangian fibrations with a giv…
Fixed loci of symplectic automorphisms of and -Kummer type manifolds
Ljudmila Kamenova, Giovanni Mongardi, Alexei Oblomkov
The aim of this paper is to give an explicit description of the fixed loci of symplectic automorphisms for certain hyperkahler manifolds, namely for Hilbert schemes on K3 surfaces…
Non-hyperbolicity of holomorphic symplectic varieties
Ljudmila Kamenova, Christian Lehn
We prove non-hyperbolicity of primitive symplectic varieties with that satisfy the rational SYZ conjecture. If in addition , we establish that the Kobayash…
Roundness of the ample cone and existence of double Lagrangian fibrations on hyperkahler manifolds
Ljudmila Kamenova, Misha Verbitsky
Let be a hyperkahler manifold of maximal holonomy (that is, an IHS manifold), and let be its Kahler cone, which is an open, convex subset in the space of re…
Kobayashi non-hyperbolicity of Calabi-Yau manifolds via mirror symmetry
Ljudmila Kamenova, Cumrun Vafa
A compact complex manifold is Kobayashi non-hyperbolic if there exists an entire curve on it. Using mirror symmetry we establish that there are (possibly singular) elliptic or rati…
Boundedness in families with applications to arithmetic hyperbolicity
Raymond van Bommel, Ariyan Javanpeykar, Ljudmila Kamenova
Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to…
Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kahler geometry
Ljudmila Kamenova, Misha Verbitsky
Let be a holomorphic symplectic Kähler manifold equipped with a Lagrangian fibration with compact fibers. The base of this manifold is equipped with a special Kähler struct…
Symplectic involutions of type and Kummer type manifolds
Ljudmila Kamenova, Giovanni Mongardi, Alexei Oblomkov
In this paper we describe the fixed locus of a symplectic involution on a hyperkähler manifold of type or of Kummer type. We prove that the fixed locus consists of f…
Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps
Ariyan Javanpeykar, Ljudmila Kamenova
Demailly's conjecture, which is a consequence of the Green-Griffiths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variet…
Twistor spaces and compact manifolds admitting both Kähler and non-Kähler structures
Ljudmila Kamenova
In this expository paper we review some twistor techniques and recall the problem of finding compact differentiable manifolds that can carry both Kähler and non-Kähler complex stru…
Algebraically hyperbolic manifolds have finite automorphism groups
Fedor Bogomolov, Ljudmila Kamenova, Misha Verbitsky
A projective manifold is algebraically hyperbolic if there exists a positive constant such that the degree of any curve of genus on is bounded from above by $A(g-1)…
Pullbacks of hyperplane sections for Lagrangian fibrations are primitive
Ljudmila Kamenova, Misha Verbitsky
Let p: M -> B be a Lagrangian fibration on a hyperkahler manifold of maximal holonomy (also known as IHS), and H the generator of the Picard group of B. We prove that the pullback…
Survey of finiteness results for hyperkähler manifolds
Ljudmila Kamenova
This paper is a survey of finiteness results in hyperkähler geometry. We review some classical theorems by Sullivan, Kollár-Matsusaka, Huybrechts, as well as theorems in the recent…
Algebraic non-hyperbolicity of hyperkahler manifolds with Picard rank greater than one
Ljudmila Kamenova, Misha Verbitsky
A projective manifold is algebraically hyperbolic if the degree of any curve is bounded from above by its genus times a constant, which is independent from the curve. This is a pro…
On the Kobayashi pseudometric, complex automorphisms and hyperkaehler manifolds
Fedor Bogomolov, Ljudmila Kamenova, Steven Lu +1
We define the Kobayashi quotient of a complex variety by identifying points with vanishing Kobayashi pseudodistance between them and show that if a compact complex manifold has an…
Finiteness of Lagrangian fibrations with fixed invariants
Ljudmila Kamenova
We prove finiteness of hyperkaehler Lagrangian fibrations in any fixed dimension with fixed Fujiki constant and discriminant of the Beauville-Bogomolov-Fujiki lattice, up to deform…
Kobayashi pseudometric on hyperkahler manifolds
Ljudmila Kamenova, Steven Lu, Misha Verbitsky
The Kobayashi pseudometric on a complex manifold is the maximal pseudometric such that any holomorphic map from the Poincaré disk to the manifold is distance-decreasing. Kobayashi…