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On the algebraic fundamental group of surfaces with K^2\leq 3χ

Margarida Mendes Lopes·Rita Pardini
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Abstract

Let S be a minimal complex surface of general type with $q(S)=0$. We prove the following statements concerning the algebraic fundamental group: I) Assume that K^2_S\leq 3χ(S). Then S has an irregular etale cover if and only if S has a free pencil of hyperelliptic curves of genus 3 with at least 4 double fibres. II) If K^2_S=3 and χ(S)=1, then S has no irregular etale cover. III) If K^2_S<3χ(S) and S does not have any irregular etale cover, then the order of the algebraic fundamental group is lesser or equal to 9, and if equality occurs then K^2_S=2, χ(S)=1.

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Margarida Mendes Lopes, Rita Pardini. 2007-03-16. On the algebraic fundamental group of surfaces with K^2\leq 3χ. https://arxiv.org/abs/math/0512483

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