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On
Kodaira fibrations with invariant cohomology
Corey Bregman |
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Geometry & Topology 25 (2021) 2385–2404
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Abstract |
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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 with nontrivial invariant –cohomology in degree , proving that if the dimension of the holomorphic invariants is or , then admits a branch covering over a product of curves inducing an isomorphism on rational cohomology in degree . 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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Keywords
Kodaira fibration, surface bundle, Albanese variety,
monodromy
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Mathematical Subject Classification 2010
Primary: 14D06, 14H15, 32Q15
Secondary: 14F40, 14J29, 20F34, 57M50
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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
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Authors |
| Corey Bregman | |
| Department of Mathematics and
Statistics University of Southern Maine Portland, ME United States |
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| https://sites.google.com/view/cbregman | |
