Deformations of rational curves on primitive symplectic varieties and applications

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-03-30 DOI:10.14231/ag-2023-006

C. Lehn, Giovanni Mongardi, Gianluca Pacienza

引用次数: 6

Abstract

We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform along their Hodge locus in the universal locally trivial deformation. As applications, we extend Markman's deformation invariance of prime exceptional divisors along their Hodge locus to this singular framework and provide existence results for uniruled ample divisors on primitive symplectic varieties which are locally trivial deformations of any moduli space of semistable objects on a projective $K3$ or fibers of the Albanese map of those on an abelian surface. We also present an application to the existence of prime exceptional divisors.

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原始辛变量上有理曲线的变形及其应用

我们研究了有理曲线在原始辛变体上的变形理论，并证明了如果有理曲线覆盖一个除数，那么，在光滑的情况下，它们在普遍局部平凡变形中沿着它们的Hodge轨迹变形。作为应用，我们将素数例外除数沿其Hodge轨迹的Markman变形不变性扩展到该奇异框架，并提供了原始辛变体上的不规则充分除数的存在性结果，这些不规则充分除数是投影$K3$上半稳定对象的任何模空间的局部平凡变形，或阿贝尔表面上那些对象的Albanese映射的纤维。我们还提出了素数例外除数存在性的一个应用。

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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.