3 citations · 5 across the 5 of their papers we have counts for
5 papers
Shafarevich-Tate groups of holomorphic Lagrangian fibrations II
Anna Abasheva
Let be a compact hyperkähler manifold with a Lagrangian fibration . A Shafarevich-Tate twist of is a holomorphic symplectic manifold with a Lagrangian fibra…
Complex surfaces with many algebraic structures
Anna Abasheva, Rodion Déev
We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve in and blow up…
Shafarevich-Tate groups of holomorphic Lagrangian fibrations
Anna Abasheva, Vasily Rogov
Consider a Lagrangian fibration on a hyperkähler manifold . There are two ways to construct a holomorphic family of deformations of over $\mathbb…
Algebraic dimension and complex subvarieties of hypercomplex nilmanifolds
Anna Abasheva, Misha Verbitsky
A nilmanifold is a (left) quotient of a nilpotent Lie group by a cocompact lattice. A hypercomplex structure on a manifold is a triple of complex structure operators satisfying the…
Feix-Kaledin metric on the total spaces of cotangent bundles to Kähler quotients
Anna Abasheva
In this paper we study the geometry of the total space of a cotangent bundle to a Kähler manifold where is obtained as a Kähler reduction from . Using the…