Fibration of $\operatorname{log}$-general type space over quasi-abelian varieties

We show that there exists no smooth fibration of a smooth complex quasi-projective variety of $\operatorname{log}$‑general type over a quasi-abelian variety. The proof uses M. Popa and C. Schnell’s construction of Higgs bundle.

Keywords

smooth fibration, logarithmic pole, holomorphic one-form, zero locus, quasi-abelian variety, Kodaira dimension, Hodge module, Higgs bundle

2010 Mathematics Subject Classification

Primary 14J99. Secondary 14D99, 14F10.

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Received 18 February 2017

Accepted 6 April 2020

Published 30 September 2021