论k模空间上CM线束的正性

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2019-12-01 DOI:10.4007/annals.2020.192.3.7

Chenyang Xu, Ziquan Zhuang

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引用次数: 49

摘要

本文考虑了k -模空间上的CM线束，即参数化k -多稳态Fano变元的模空间。证明了它在任何适当的子空间上都是充足的，这些子空间的参数化简化一致k -稳定的Fano变应该是整个模空间。作为推论，我们证明了模空间参数化光滑k -多稳态Fano变簇是射影的。在证明过程中，我们开发了一个新的过滤不变量，它可以用来检验Fano变量的各种k -稳定性概念。

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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On positivity of the CM line bundle on K-moduli spaces

In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace parametrizing reduced uniformly K-stable Fano varieties which conjecturally should be the entire moduli space. As a corollary, we prove that the moduli space parametrizing smoothable K-polystable Fano varieties is projective. During the course of proof, we develop a new invariant for filtrations which can be used to test various K-stability notions of Fano varieties.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.