Volume 25, issue 5 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
On Kodaira fibrations with invariant cohomology

Corey Bregman

Geometry & Topology 25 (2021) 2385–2404
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.

Keywords
Kodaira fibration, surface bundle, Albanese variety, monodromy
Mathematical Subject Classification 2010
Primary: 14D06, 14H15, 32Q15
Secondary: 14F40, 14J29, 20F34, 57M50
References
Publication
Received: 18 April 2019
Revised: 7 August 2020
Accepted: 8 September 2020
Published: 3 September 2021
Proposed: Jim Bryan
Seconded: Dan Abramovich, Benson Farb
Authors
Corey Bregman
Department of Mathematics and Statistics
University of Southern Maine
Portland, ME
United States
https://sites.google.com/view/cbregman