Quotients of the square of a curve by a mixed action, further quotients and Albanese morphisms

2017/08/05 by Pignatelli, Roberto
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.01750

Abstract

We study mixed surfaces, the minimal resolution S of the singularities of a quotient (C x C)/G of the "square" of a curve by a finite group G of automorphisms that contains elements not preserving the factors. We study them through the "further quotients" by (C x C)/G' where G' contains G. As a first application we prove that if the irregularity is at least 3, then S is also minimal. The result is sharp. The main result is a complete description of the Albanese morphism of S through a determined further quotient (C x C)/G' that is an étale cover of the symmetric square of a curve. In particular, if the irregularity of S is at least 2, then S has maximal Albanese dimension. We apply our result to all the "semi-isogenous" mixed surfaces of maximal Albanese dimension constructed by Cancian and Frapporti, relating them with the other constructions appearing in the literature of surfaces of general type having the same invariants.

Related

• Mixed quasi-étale quotients with arbitrary singularities
• Mixed quasi-étale surfaces, new surfaces of general type with p_g=0 and their fundamental group
• On Semi-isogenous mixed surfaces
• Quotients of products of curves, new surfaces with p_g=0 and their fundamental groups
• On regular surfaces of general type with numerically trivial automorphism group of order 4