Výsledky vyhledávání - "Abasheva, Anna"

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Shafarevich-Tate groups of holomorphic Lagrangian fibrations II

Autor: Abasheva, Anna

Let $X$ be a compact hyperk\"ahler manifold with a Lagrangian fibration $\pi\colon X\to B$. A Shafarevich-Tate twist of $X$ is a holomorphic symplectic manifold with a Lagrangian fibration $\pi^\varphi\colon X^\varphi\to B$ which is isomorphic to $\p

Externí odkaz: http://arxiv.org/abs/2407.09178

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Complex surfaces with many algebraic structures

Autor: Abasheva, Anna, Déev, Rodion

We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve $E$ in $\mathbb P^2$ and blow up nine general points on $E$. Then the complement $M$ of the strict tran

Externí odkaz: http://arxiv.org/abs/2303.10764

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Shafarevich-Tate groups of holomorphic Lagrangian fibrations

Autor: Abasheva, Anna, Rogov, Vasily

Consider a Lagrangian fibration $\pi\colon X\to \mathbb P^n$ on a hyperk\"ahler manifold $X$. There are two ways to construct a holomorphic family of deformations of $\pi$ over $\mathbb C$. The first one is known under the name Shafarevich-Tate famil

Externí odkaz: http://arxiv.org/abs/2112.10921

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Algebraic dimension and complex subvarieties of hypercomplex nilmanifolds

Autor: Abasheva, Anna, Verbitsky, Misha

Publikováno v: Adv. in Math., Vol. 414, 1 Feb 2023, 108866

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 quaternionic relations. A hypercomplex nilmanifold is a compact quoti

Externí odkaz: http://arxiv.org/abs/2103.05528

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Feix-Kaledin metric on the total spaces of cotangent bundles to K\'ahler quotients

Autor: Abasheva, Anna

Publikováno v: Int. Math. Res. Not., 2021, rnab047

In this paper we study the geometry of the total space $Y$ of a cotangent bundle to a K\"ahler manifold $N$ where $N$ is obtained as a K\"ahler reduction from $\mathbb C^n$. Using the hyperk\"ahler reduction we construct a hyperk\"ahler metric on $Y$

Externí odkaz: http://arxiv.org/abs/2007.05773

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