On Kodaira fibrations with invariant cohomology

Corey Bregman

doi:10.2140/gt.2021.25.2385

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arXiv · 1811.00584

On Kodaira fibrations with invariant cohomology

Corey Bregman

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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 rational 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. 2018-11-01. On Kodaira fibrations with invariant cohomology. https://doi.org/10.2140/gt.2021.25.2385

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