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arXiv · 1801.02562

Vanishing theorems for parabolic Higgs bundles

Donu Arapura·Feng Hao·Hongshan Li
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Abstract

This is a sequel to "Kodaira-Saito vanishing via Higgs bundles in positive characteristic" (arXiv:1611.09880). However, unlike the previous paper, all the arguments here are in characteristic zero. The main result is a Kodaira vanishing theorem for semistable parabolic Higgs bundles with trivial parabolic Chern classes. This implies a general semipositivity theorem. This also implies a Kodaira-Saito vanishing theorem for complex variations of Hodge structure.

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Donu Arapura, Feng Hao, Hongshan Li. 2018-01-08. Vanishing theorems for parabolic Higgs bundles. https://arxiv.org/abs/1801.02562

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