Hyper-Kahler Manifolds of Generalized Kummer Type and the Kuga-Satake Correspondence

Varesco M.; Voisin C.

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Hyper-Kahler Manifolds of Generalized Kummer Type and the Kuga-Satake Correspondence

机译：广义Kummer型的Hyper-Kahler流形和Kuga-Satake对应关系

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摘要

We first describe the construction of the Kuga-Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kahler type. We describe the classical cases where the Kuga-Satake correspondence between a hyper-Kahler manifold and its Kuga-Satake variety has been proved to be algebraic. We then turn to recent work of O'Grady and Markman which we combine to prove that the Kuga-Satake correspondence is algebraic for projective hyper-Kahler manifolds of generalized Kummer deformation type.

机译：我们首先描述了与超 Kahler 型的（极化）权重 2 的 Hodge 结构相关的 Kuga-Satake 变体的构造。我们描述了经典案例，其中超 Kahler 流形与其 Kuga-Satake 变体之间的 Kuga-Satake 对应关系已被证明是代数的。然后，我们转向 O'Grady 和 Markman 最近的工作，我们将这些工作结合起来证明 Kuga-Satake 对应关系是广义 Kummer 变形类型的射影超 Kahler 流形的代数。

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来源
《Milan Journal of Mathematics》 |2022年第2期|433-444|共12页
作者
Varesco M.; Voisin C.;
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作者单位

Univ Bonn Rheinische Friedrich Wilhelms Univ Bonn;

Math Inst Jussieu Paris Rive Gauche;

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原文格式 PDF
正文语种英语
中图分类数学;
关键词
ABELIAN-VARIETIES; HYPERKAHLER MANIFOLDS;

机译：阿贝利亚品种;HYPERBALD 歧管;

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Hyper-Kahler Manifolds of Generalized Kummer Type and the Kuga-Satake Correspondence

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