Inducing Coverings on Hilbert Schemes

IF 1 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2026-08-07 Epub Date: 2026-07-22 DOI:10.1002/mana.70186

Lucas Li Bassi, Filippo Papallo

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引用次数: 0

Abstract

We find an explicit geometric description of all coverings of ${Hilb}^{2} (Σ)$ when $Σ$ is a normal, complex, quasi-projective surface with finite fundamental group. We then apply this construction to show that if $Σ$ is an irreducible symplectic surface then ${Hilb}^{2} (Σ)$ is an irreducible symplectic variety.

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希尔伯特方案的诱导覆盖

我们找到了Hilb 2 （Σ）$ \operatorname{Hilb}^{2}(\Sigma)$的所有覆盖的显式几何描述，当Σ $\Sigma$是一个正常的，复的，具有有限基群的拟射影曲面。然后我们应用这个构造来证明如果Σ $\Sigma$是一个不可约的辛曲面，那么Hilb 2 （Σ）$ \operatorname{Hilb}^{2}(\Sigma)$也是一种不可约辛变异体。

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index