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

IF 1.2 3区数学 Q1 MATHEMATICS

Milan Journal of Mathematics Pub Date : 2022-01-01 Epub Date: 2022-10-19 DOI:10.1007/s00032-022-00369-8

M Varesco, C Voisin

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引用次数: 2

摘要

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。

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

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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来源期刊

Milan Journal of Mathematics 数学-数学

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists. Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.