Fundamental Group of some Genus-2 Fibrations and Applications

R. V. Gurjar; Sagar Kolte

doi:10.1142/S0129167X12500802

Fundamental Group of some Genus-2 Fibrations and Applications

Algebraic Geometry 2015-12-31 v1

Authors: 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 $\pi_1(C) \times \pi_1(E)$ , 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 $b_1(X)>b_1(C)$ .

Keywords

genus-2 fibration fundamental group smooth projective surface elliptic curve Shafarevich conjecture holomorphic convexity universal cover

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@article{arxiv.1512.08839,
  title  = {Fundamental Group of some Genus-2 Fibrations and Applications},
  author = {R. V. Gurjar and Sagar Kolte},
  journal= {arXiv preprint arXiv:1512.08839},
  year   = {2015}
}

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23 Pages, Published in the International Journal of Mathematics

Fundamental Group of some Genus-2 Fibrations and Applications

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