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

Sönke Rollenske

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

Algebraic Geometry 2014-04-29 v1

Authors: Sönke Rollenske

Abstract

We construct from a general del Pezzo surface of degree 1 a Gorenstein stable surfaces $X$ 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.

Keywords

stable Godeaux surfaces moduli space irreducible component del Pezzo surface Gorenstein stable surfaces canonical ring pluricanonical maps

Cite

@article{arxiv.1404.7027,
  title  = {A new irreducible component of the moduli space of stable Godeaux surfaces},
  author = {Sönke Rollenske},
  journal= {arXiv preprint arXiv:1404.7027},
  year   = {2014}
}

Comments

12 pages, 4 figures

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