Twisted Hodge filtration: Curvature of the determinant

Philipp Naumann

Mathematische Nachrichten, 2019, vol. 292, issue 11, 2452-2455

Abstract: Given a holomorphic family f:X→S of compact complex manifolds and a relatively ample line bundle L→X, the higher direct images Rn−pf∗ΩX/Sp(L) carry a natural hermitian metric. An explicit formula for the curvature tensor of these direct images is given in [8]. We prove that the determinant of the twisted Hodge filtration FLp=⨁i≥pRn−if∗ΩX/Si(L) is (semi‐)positive on the base S if L itself is (semi‐)positive on X.

Date: 2019
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https://doi.org/10.1002/mana.201800418

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