Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles

IF 0.9 Q2 MATHEMATICS Epijournal de Geometrie Algebrique Pub Date : 2018-09-22 DOI:10.46298/epiga.2022.6577
Y. Hashimoto, Julien Keller
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引用次数: 4

Abstract

For a holomorphic vector bundle $E$ over a polarised K\"ahler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In particular, we provide an explicit estimate which proves that Donaldson's functional is coercive on the set of Fubini-Study metrics if $E$ is slope stable, and give a new proof of Hermitian-Einstein metrics implying slope stability.
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向量束的Fubini-Study度量和Donaldson泛函的报价方案极限
对于极化K\ ahler流形上的全纯向量束$E$,我们通过定义ubinii - study度量的quote -scheme极限,建立了$E$的斜率稳定性与Donaldson泛函的渐近行为之间的直接联系。特别地,我们给出了一个显式估计,证明了如果$E$是边坡稳定的,则在Fubini-Studymetrics集上Donaldson泛函是强制的,并给出了Hermitian-Einsteinmetrics暗示边坡稳定的新证明。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
19
审稿时长
25 weeks
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