ω-trace and Griffiths positivity for singular Hermitian metrics

2024/02/05 by Watanabe, Yuta
#32L10 #32L20 #32Q10 #32U05 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.06658

Abstract

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

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