Involutions on surfaces with p_g=q=1

2008/05/29 by Carlos Rito, Rito, Carlos
Mathematics · #14J29 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.0805.4513

openalex publication_date 2008/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general type S with p_g=q=1 having an involution i such that S/i is a non-ruled surface and such that the bicanonical map of S is not composed with i. A complete list of possibilities is given and several new examples are constructed, as bidouble covers of surfaces. In particular the first example of a minimal surface of general type with p_g=q=1 and K²=7 having birational bicanonical map is obtained.

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