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arXiv · 2302.09398

Dual Nakano positivity and singular Nakano positivity of direct image sheaves

Yuta Watanabe
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Abstract

Let $f:X\to Y$ be a surjective projective map and $L$ be a holomorphic line bundle on $X$ equipped with a (singular) semi-positive Hermitian metric $h$. In this article, by studying the canonical metric on the direct image sheaf of the twisted relative canonical bundles $K_{X/Y}\otimes L\otimes\mathscr{I}(h)$, we obtain that this metric has dual Nakano semi-positivity when $h$ is smooth and there is no deformation by $f$ and that this metric has locally Nakano semi-positivity in the singular sense when $h$ is singular.

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Yuta Watanabe. 2023-02-18. Dual Nakano positivity and singular Nakano positivity of direct image sheaves. https://doi.org/10.1017/nmj.2024.20

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