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Twisted Hodge filtration: Curvature of the determinant
Author(s) -
Naumann Philipp
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800418
Subject(s) - mathematics , filtration (mathematics) , pure mathematics , curvature , holomorphic function , line bundle , riemann curvature tensor , hermitian matrix , hermitian manifold , mathematical analysis , geometry , ricci curvature
Given a holomorphic family f : X → S of compact complex manifolds and a relatively ample line bundle L → X , the higher direct imagesR n − pf ∗ Ω X / S p ( 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 filtrationF L p = ⨁ i ≥ pR n − if ∗ Ω X / S i ( L )is (semi‐)positive on the base S if L itself is (semi‐)positive on X .