Quot-scheme limit of Fubini-Study metrics and its applications to balanced metrics

Autor:	Hashimoto, Yoshinori, Keller, Julien
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry Mathematics - Complex Variables Mathematics - Differential Geometry 14J60 14L24 53C07
Druh dokumentu:	Working Paper
Popis:	We present some results that complement our prequels [arXiv:1809.08425,arXiv:1907.05770] on holomorphic vector bundles. We apply the method of the Quot-scheme limit of Fubini-Study metrics developed therein to provide a generalisation to the singular case of the result originally obtained by X.W. Wang for the smooth case, which states that the existence of balanced metrics is equivalent to the Gieseker stability of the vector bundle. We also prove that the Bergman 1-parameter subgroups form subgeodesics in the space of hermitian metrics. This paper also contains a review of techniques developed in [arXiv:1809.08425,arXiv:1907.05770] and how they correspond to their counterparts developed in the study of the Yau-Tian-Donaldson conjecture. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2101.00996 Zobrazit plný text záznamu View this record from Arxiv