A new irreducible component of the moduli space of stable Godeaux surfaces

2014/04/28 by Rollenske, Sönke
#14J10 #14J25 #14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.7027

Abstract

We construct from a general del Pezzo surface of degree 1 a Gorenstein stable surfaces X with K_X²=1 and p_g(X)=q(X)=0. These surfaces are not smoothable but give an open subset of an irreducible component of the moduli space of stable Godeaux surfaces. In a particular example we also compute the canonical ring explicitly and discuss the behaviour of pluricanonical maps.

Related

• Canonical rings of Gorenstein stable Godeaux surfaces
• Gorenstein stable Godeaux surfaces
• Gorenstein stable surfaces with K_X² =1 and χ(\mathcal O_X) =2
• Godeaux surfaces with an Enriques involution and some stable degenerations
• Smoothing semi-smooth Stable Godeaux surfaces