Curvature operator of holomorphic vector bundles and $L^2$-estimate condition for $(n,q)$ and $(p,n)$-forms

Yuta Watanabe

Curvature operator of holomorphic vector bundles and $L^2$-estimate condition for $(n,q)$ and $(p,n)$-forms

Differential Geometry 2022-06-24 v2

Authors: Yuta Watanabe

Abstract

We study the positivity properties of the curvature operator for holomorphic Hermitian vector bundles. We obtain new characterization of semi-positive curvature operators for $(n,q)$ and $(p,n)$ -forms by L2-estimates. The characterization of Nakano semi-positivity by $L^2$ -estimate is already known. Applying our results, we give new characterizations of Nakano semi-negativity.

Keywords

curvature operator holomorphic vector bundles L^2-estimate semi-positivity Nakano semi-negativity (n,q)-forms (p,n)-forms

Cite

@article{arxiv.2109.12554,
  title  = {Curvature operator of holomorphic vector bundles and $L^2$-estimate condition for $(n,q)$ and $(p,n)$-forms},
  author = {Yuta Watanabe},
  journal= {arXiv preprint arXiv:2109.12554},
  year   = {2022}
}

Comments

26 pages

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