On Kodaira fibrations with invariant cohomology

Bregman, Corey¹

¹ Department of Mathematics and Statistics, University of Southern Maine, Portland, ME, United States

Geometry & topology, Tome 25 (2021) no. 5, pp. 2385-2404.

Résumé

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 $\mathbb{Q}$–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.

Détail

DOI : 10.2140/gt.2021.25.2385

Classification : 14D06, 14H15, 32Q15, 14F40, 14J29, 20F34, 57M50
Keywords: Kodaira fibration, surface bundle, Albanese variety, monodromy

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