Involutions on surfaces with p_g=q=0 and K²=3

2010/07/28 by Carlos Rito, Rito, Carlos
Mathematics · #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1007.5036

openalex publication_date 2010/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study surfaces of general type S with p_g=0 and K²=3 having an involution i such that the bicanonical map of S is not composed with i. It is shown that, if S/i is not rational, then S/i is birational to an Enriques surface or it has Kodaira dimension 1 and the possibilities for the ramification divisor of the covering map S→ S/i are described. We also show that these two cases do occur, providing an example. In this example S has a hyperelliptic fibration of genus 3 and the bicanonical map of S is of degree 2 onto a rational surface.

Citations

• On the computation of singular plane curves and quartic surfaces

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