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arXiv · 1709.03164

Monodromy of Kodaira Fibrations of Genus $3$

Laure Flapan
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Abstract

A Kodaira fibration is a non-isotrivial fibration $f\colon S\rightarrow B$ from a smooth algebraic surface $S$ to a smooth algebraic curve $B$ such that all fibers are smooth algebraic curves of genus $g$. Such fibrations arise as complete curves inside the moduli space $\mathcal{M}_g$ of genus $g$ algebraic curves. We investigate here the possible connected monodromy groups of a Kodaira fibration in the case $g=3$ and classify which such groups can arise from a Kodaira fibration obtained as a general complete intersection curve inside a subvariety of $\mathcal{M}_3$ parametrizing curves whose Jacobians have extra endomorphisms.

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Laure Flapan. 2017-09-10. Monodromy of Kodaira Fibrations of Genus $3$. https://arxiv.org/abs/1709.03164

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