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arXiv · 1512.08839

Fundamental Group of some Genus-2 Fibrations and Applications

R. V. Gurjar·Sagar Kolte
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Abstract

We will prove that given a genus-2 fibration $f: X \rightarrow C$ on a smooth projective surface $X$ such that $b_1(X)=b_1(C)+2$, the fundamental group of $X$ is almost isomorphic to $π_1(C) \times π_1(E)$, where $E$ is an elliptic curve. We will also verify the Shafarevich Conjecture on holomorphic convexity of the universal cover of surfaces $X$ with genus-2 fibration $X\rightarrow C$ such that $b_1(X)>b_1(C)$.

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R. V. Gurjar, Sagar Kolte. 2015-12-30. Fundamental Group of some Genus-2 Fibrations and Applications. https://doi.org/10.1142/s0129167x12500802

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