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arXiv · 1406.6308

Dihedral Monodromy and Xiao Fibrations

Alberto Albano·Gian Pietro Pirola
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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 \'etale 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.

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Alberto Albano, Gian Pietro Pirola. 2014-06-24. Dihedral Monodromy and Xiao Fibrations. https://doi.org/10.1007/s10231-015-0514-y

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