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2021 On Kodaira fibrations with invariant cohomology
Corey Bregman
Geom. Topol. 25(5): 2385-2404 (2021). DOI: 10.2140/gt.2021.25.2385

Abstract

A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant –cohomology in degree 1, proving that if the dimension of the holomorphic invariants is 1 or 2, then X admits a branch covering over a product of curves inducing an isomorphism on rational cohomology in degree 1. We also study the class of Kodaira fibrations possessing a holomorphic section, and demonstrate that having a section imposes no restriction on possible monodromies.

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Corey Bregman. "On Kodaira fibrations with invariant cohomology." Geom. Topol. 25 (5) 2385 - 2404, 2021. https://doi.org/10.2140/gt.2021.25.2385

Information

Received: 18 April 2019; Revised: 7 August 2020; Accepted: 8 September 2020; Published: 2021
First available in Project Euclid: 12 October 2021

Digital Object Identifier: 10.2140/gt.2021.25.2385

Subjects:
Primary: 14D06, 14H15, 32Q15
Secondary: 14F40, 14J29, 20F34, 57M50

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 5 • 2021
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