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

Yuta Watanabe

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arXiv · 2109.12554

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

Yuta Watanabe

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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.

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BibTeX RIS

Yuta Watanabe. 2021-09-26. Curvature operator of holomorphic vector bundles and $L^2$-estimate condition for $(n,q)$ and $(p,n)$-forms. https://arxiv.org/abs/2109.12554

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