A new irreducible component of the moduli space of stable Godeaux   surfaces
  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. 
S\"onke Rollenske
math.AG