Dihedral Monodromy and Xiao Fibrations

Abstract

We construct three new families of fibrations $\pi :S\to B$ where $S$ is an algebraic complex surface and $B$ a curve that violate Xiao's conjecture relating the relative irregularity and the genus of the general fiber. The fibers of $\pi$ are certain étale cyclic covers of hyperelliptic curves that give coverings of $P^1$ with dihedral monodromy. As an application, we also show the existence of big and nef effective divisors in the Brill-Noether range.

arXiv comment12 pages. Exposition improved. The last section has been expanded with more details of the proof. Accepted for publication in Ann. Mat. Pura Appl

Cited by in corpus (7)

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• Xiao's conjecture for general fibred surfaces
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• Fibred surfaces and their unitary rank
• Locally non-trivial fibred surfaces with maximal unitary rank
• On the rank of the flat unitary summand of the Hodge bundle
• Explicit analysis of positive dimensional fibres of ${\mathcal{P}}_{g,r}$ and Xiao conjecture