$\omega$-trace and Griffiths positivity for singular Hermitian metrics

Yuta Watanabe

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arXiv · 2402.06658

$\omega$-trace and Griffiths positivity for singular Hermitian metrics

Yuta Watanabe

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Abstract

In this paper, we investigate various positivity for singular Hermitian metrics such as Griffiths, $\omega$-trace and RC, where $\omega$ is a Hermitian metric, and show that these quasi-positivity notions induce $0$-th cohomology vanishing, rational conected-ness, etc. Here, $\omega$-trace positivity of smooth Hermitian metrics $h$ on holomorphic vector bundles $E$ represents the positivity of $tr_\omega i\Theta_{E,h}$.

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BibTeX RIS

Yuta Watanabe. 2024-02-05. $\omega$-trace and Griffiths positivity for singular Hermitian metrics. https://arxiv.org/abs/2402.06658

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