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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 Epub Date: 2022-10-19 DOI:10.1007/s00032-022-00369-8

M Varesco, C Voisin

引用次数: 2

Abstract

We first describe the construction of the Kuga-Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga-Satake correspondence between a hyper-Kähler 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-Kähler manifolds of generalized Kummer deformation type.

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Hyper-Kähler广义Kummer型流形与Kuga-Satake对应。

我们首先描述了与hyper-Kähler型(极化)权重二Hodge结构相关的Kuga-Satake品种的构建。我们描述了证明hyper-Kähler流形与其Kuga-Satake变体之间的Kuga-Satake对应是代数的经典情况。然后，我们转向O'Grady和Markman最近的工作，我们将其结合起来证明Kuga-Satake对应是广义Kummer变形型投影hyper-Kähler流形的代数对应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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