On the algebraic fundamental group of surfaces with K²≤ 3χ

2005/12/21 by Margarida Mendes Lopes, Rita Pardini, Lopes, Margarida Mendes +1
Mathematics · #14F35 #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · doi:10.48550/arxiv.math/0512483

openalex publication_date 2005/12/21 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

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 K²_S≤ 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 K²_S=3 and χ(S)=1, then S has no irregular etale cover. III) If K²_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 K²_S=2, χ(S)=1.

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