A variational approach to the Hermitian-Einstein metrics and the Quot-scheme limit of Fubini-Study metrics

2019/07/12 by Yoshinori Hashimoto, Hashimoto, Yoshinori, Julien Keller +1
Mathematics · #14J60 #14L24 #53C07 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.CV #math.DG #msc:14J60 #msc:14L24 #msc:53C07

paper · pdf · doi:10.48550/arxiv.1907.05770

33 pages

arxiv created 2019/07/12 · arxiv updated 2019/07/15

Abstract

This is a sequel of our paper [arXiv:1809.08425] on the Quot-scheme limit and variational properties of Donaldson's functional, which established its coercivity for slope stable holomorphic vector bundles over smooth projective varieties. Assuming that the coercivity is uniform in a certain sense, we provide a new proof of the Donaldson-Uhlenbeck-Yau theorem, in such a way that the analysis involved in the proof is elementary except for the asymptotic expansion of the Bergman kernel.

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