Note on a family of surfaces with p_g=q=2 and K²=7

2020/12/10 by Penegini, Matteo, Pignatelli, Roberto
#14B12 (Secondary) #14J29 (Primary) 14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.05636

Abstract

We study a family of surfaces of general type with p_g=q=2 and K²=7, originally constructed by C. Rito. We provide an alternative construction of these surfaces, that allows us to describe their Albanese map and the corresponding locus M in the moduli space of the surfaces of general type. In particular we prove that M is an open subset, and it has three connected components, two dimensional, irreducible and generically smooth.

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