The bicanonical map of surfaces with p_g=0 and K²≥ 7, II

2001/11/13 by Margarida Mendes Lopes, Rita Pardini, Lopes, Margarida Mendes +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.math/0111160

Latex 2e, 8 pages

arxiv created 2001/11/13 · arxiv updated 2009/11/30

Abstract

We study the minimal complex surfaces of general type with p_g=0 and K²=7 or 8 whose bicanonical map is not birational. In the paper 'The bicanonical map of surfaces with p_g=0 and K²≥ 7' we have shown that if S is such a surface, then the bicanonical map has degree 2. Here we describe precisely such surfaces showing that there is a fibration f\colon S→ \pp¹ such that: i) the general fibre F of f is a genus 3 hyperelliptic curve; ii) the involution induced by the bicanonical map of S restricts to the hyperelliptic involution of F. Furthermore, if K²_S=8, then f is an isotrivial fibration with 6 double fibres, and if K²_S=7, then f has 5 double fibres and it has precisely one fibre with reducible support, consisting of two components.

Related

• The bicanonical map of surfaces with p_g=0 and K² ≥ 7
• A new family of surfaces with p_g=0 and K²=3
• The classification of surfaces with p_g=0, K²=6 and non birational bicanonical map
• A survey on the bicanonical map of surfaces with p_g=0 and K²≥ 2
• The degree of the bicanonical map of a surface with p_g=0