Abstract
We construct from a general del Pezzo surface of degree 1 a Gorenstein stable surface X with \({K_X^2=1}\) 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.
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Rollenske, S. A new irreducible component of the moduli space of stable Godeaux surfaces. manuscripta math. 149, 117–130 (2016). https://doi.org/10.1007/s00229-015-0776-0
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DOI: https://doi.org/10.1007/s00229-015-0776-0