Admissible metrics on compact K\"ahler varieties

Wenhao Ou

Admissible metrics on compact K\"ahler varieties

Algebraic Geometry 2022-08-19 v2 Differential Geometry

Authors: Wenhao Ou

Abstract

Let $X$ be a normal compact K\"ahler variety, and $\mathcal{F}$ a coherent reflexive sheaf on $X$ . We investigate the existence of admissible Hermitian metrics on $\mathcal{F}$ . If moreover $\mathcal{F}$ is slope stable, we also study the existence of admissible Hermitian-Yang-Mills metrics on it. The existence will hold if one can prove a uniform Sobolev inequality on singular spaces.

Keywords

compact kähler varieties coherent reflexive sheaf admissible hermitian metrics slope stable hermitian-yang-mills metrics sobolev inequality

Cite

@article{arxiv.2201.04821,
  title  = {Admissible metrics on compact K\"ahler varieties},
  author = {Wenhao Ou},
  journal= {arXiv preprint arXiv:2201.04821},
  year   = {2022}
}

Comments

The proof of uniform Sobolev inequality in the first version contains a serious gap. We could not fix it, and propose it as a conjecture in the new version. Therefore, the proof on the existence of HYM metrics in the first version is not complete

Admissible metrics on compact K\"ahler varieties

Abstract

Keywords

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