Surfaces with K²=2X-2 and p_g≥ 5

2010/03/17 by Sanchez, Maria Marti
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1003.3469

Abstract

This note describes minimal surfaces S of general type satisfying p_g≥ 5 and K²=2p_g. For p_g≥ 8 the canonical map of such surfaces is generically finite of degree 2 and the bulk of the paper is a complete characterization of such surfaces with non birational canonical map. It turns out that if p_g≥ 13, S has always an (unique) genus 2 fibration, whose non 2-connected fibres can be characterized, whilst for p_g≤ 12 there are two other classes of such surfaces with non birational canonical map.

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