On Semi-isogenous mixed surfaces

2015/10/30 by Cancian, Nicola, Frapporti, Davide
#14J29 #14Q10 #58E40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.09055

Abstract

Let C be a smooth projective curve and G a finite subgroup of Aut(C)²\rtimes \mathbb Z₂ whose action is mixed, i.e.~there are elements in G exchanging the two isotrivial fibrations of C× C. Let G⁰\triangleleft G be the index two subgroup G\capAut(C)². If G⁰ acts freely, then X:=(C× C)/G is smooth and we call it semi-isogenous mixed surface. In this paper we give an algorithm to determine semi-isogenous mixed surfaces with given geometric genus, irregularity and self-intersection of the canonical class. As an application we classify irregular semi-isogenous mixed surfaces with K²>0 and geometric genus equal to the irregularity; the regular case is subjected to some computational restrictions. In this way we construct new examples of surfaces of general type with χ=1. We provide an example of a minimal surface of general type with K²=7 and p_g=q=2.

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