Fano流形的Seshadri常数和K稳定性

IF 2.3 1区数学 Q1 MATHEMATICS Duke Mathematical Journal Pub Date : 2021-01-22 DOI:10.1215/00127094-2022-0026

Hamid Abban, Ziquan Zhuang

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引用次数: 10

摘要

我们给出了用Seshadri常数表示的大量线束的$\ δ $不变量的下界。作为应用，我们证明了任意大指数的无穷多族Fano超曲面的一致k -稳定性，以及Picard数1的光滑Fano三倍的大多数族的一致k -稳定性。

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Seshadri constants and K-stability of Fano manifolds

We give a lower bound of the $\delta$-invariants of ample line bundles in terms of Seshadri constants. As applications, we prove the uniform K-stability of infinitely many families of Fano hypersurfaces of arbitrarily large index, as well as the uniform K-stability of most families of smooth Fano threefolds of Picard number one.

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