通过容许标志测定法诺品种的k稳定性

IF 2.8 1区数学 Q1 MATHEMATICS

Forum of Mathematics Pi Pub Date : 2020-03-30 DOI:10.1017/fmp.2022.11

Hamid Abban, Ziquan Zhuang

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引用次数: 46

摘要

摘要本文提出了一种证明Fano品种k稳定性的一般方法。新理论用于(a)证明在Fano指标2的所有光滑Fano超曲面上Kähler-Einstein度量的存在性，(b)计算广义Eckardt点和所有点的三次曲面的超曲面的稳定性阈值，以及(c)在其他应用中提供Tian的k稳定性判据的新的代数证明。

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K-stability of Fano varieties via admissible flags

Abstract We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic surfaces at all points, and (c) provide a new algebraic proof of Tian’s criterion for K-stability, amongst other applications.

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来源期刊

Forum of Mathematics Pi Mathematics-Statistics and Probability

CiteScore

3.50

自引率

0.00%

发文量

审稿时长

19 weeks

期刊介绍： Forum of Mathematics, Pi is the open access alternative to the leading generalist mathematics journals and are of real interest to a broad cross-section of all mathematicians. Papers published are of the highest quality. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas are welcomed. All published papers are free online to readers in perpetuity.