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arXiv · 1612.00757

Twisted Hodge filtration: Curvature of the determinant

Philipp Naumann
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Abstract

Given a holomorphic family $f:\mathcal{X} \to S$ of compact complex manifolds and a relative ample line bundle $L\to \mathcal{X}$, the higher direct images $R^{n-p}f_*\Omega^p_{\mathcal{X}/S}(L)$ carry a natural hermitian metric. Using the explicit formula for the curvature tensor of these direct images, we prove that the determinant of the twisted Hodge filtration $F^p_L=\oplus_{i\geq p}R^{n-i}\Omega^i_{\mathcal{X}/S}(L)$ is (semi-) positive on the base $S$ if $L$ itself is (semi-) positive on $\mathcal{X}$.

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Philipp Naumann. 2016-12-02. Twisted Hodge filtration: Curvature of the determinant. https://arxiv.org/abs/1612.00757

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