The Kobayashi-Hitchin correspondence for nef and big classes

Satoshi Jinnouchi

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arXiv · 2603.10312

The Kobayashi-Hitchin correspondence for nef and big classes

Satoshi Jinnouchi

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Abstract

In this paper, we establish the Kobayashi-Hitchin correspondence for nef and big cohomology classes by introducing the notions of adapted closed positive $(1,1)$-currents and adapted Hermitian-Yang-Mills metrics. As applications, we investigate the equality cases of both the Bogomolov-Gieseker inequality for semistable reflexive sheaves with respect to big classes admitting a bimeromorphic Zariski decomposition and the Miyaoka-Yau inequality for projective varieties with big anti-canonical divisor.

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BibTeX RIS

Satoshi Jinnouchi. 2026-03-11. The Kobayashi-Hitchin correspondence for nef and big classes. https://arxiv.org/abs/2603.10312

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