Slope Stable Sheaves and Hermitian-Einstein Metrics on Normal Varieties with Big Cohomology Classes

Fuente: arXiv
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Main Author: Jinnouchi, Satoshi
Format: Preprint
Published: 2025
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author Jinnouchi, Satoshi
author_facet Jinnouchi, Satoshi
contents In this paper, we introduce the notions of slope stability and the Hermitian Einstein metric for big cohomology classes. The main result is the Kobayashi Hitchin correspondence on compact normal spaces with big classes admitting the birational Zariski decomposition with semiample positive part. We also prove the Bogomolov Gieseker inequality for slope stable sheaves with respect to big and nef classes. Through this paper, the bimeromorphic invariance of slope stability and the existence of Hermitian Einstein metrics plays an essential role.
format Preprint
id arxiv_https___arxiv_org_abs_2501_04910
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Slope Stable Sheaves and Hermitian-Einstein Metrics on Normal Varieties with Big Cohomology Classes
Jinnouchi, Satoshi
Algebraic Geometry
Differential Geometry
14E30, 53C07,
In this paper, we introduce the notions of slope stability and the Hermitian Einstein metric for big cohomology classes. The main result is the Kobayashi Hitchin correspondence on compact normal spaces with big classes admitting the birational Zariski decomposition with semiample positive part. We also prove the Bogomolov Gieseker inequality for slope stable sheaves with respect to big and nef classes. Through this paper, the bimeromorphic invariance of slope stability and the existence of Hermitian Einstein metrics plays an essential role.
title Slope Stable Sheaves and Hermitian-Einstein Metrics on Normal Varieties with Big Cohomology Classes
topic Algebraic Geometry
Differential Geometry
14E30, 53C07,
url https://arxiv.org/abs/2501.04910