Mathematical Research Letters

Volume 26 (2019)

Number 5

Vanishing theorems for parabolic Higgs bundles

Pages: 1251 – 1279

DOI: https://dx.doi.org/10.4310/MRL.2019.v26.n5.a1

Authors

Donu Arapura (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Feng Hao (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Hongshan Li (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Abstract

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.

D. Arapura partially supported by a grant from the Simon’s Foundation.

Received 15 January 2018

Accepted 29 August 2018

Published 27 November 2019