2-Gorenstein stable surfaces with K_X² = 1 and χ(X) = 3

2024/09/12 by Coughlan, Stephen, Franciosi, Marco, Pardini, Rita +1
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.07854

Abstract

The compactification M_1,3 of the Gieseker moduli space of surfaces of general type with K_X² =1 and χ(X)=3 in the moduli space of stable surfaces parametrises so-called stable I-surfaces. We classify all such surfaces which are 2-Gorenstein into four types using a mix of algebraic and geometric techniques. We find a new divisor in the closure of the Gieseker component and a new irreducible component of the moduli space.

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