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.

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

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