A new family of surfaces with $p_g=0$ and $K^2=3$

Details A new family of surfaces with $p_g=0$ and $K^2=3$ A new family of surfaces with $p_g=0$ and $K^2=3$

2003-04-14

arxiv.org/abs/math/0304181v1

Mathematics

Algebraic Geometry

Latex, 36 pages

Scientific paper

Let S be a minimal complex surface of general type with p_g=0 such that the bicanonical map of S is not birational and let Z be the bicanonical image. In [M.Mendes Lopes, R.Pardini, "Enriques surfaces with eight nodes", Math. Zeit. 241 (4) (2002), 673-683] it is shown that either: i) Z is a rational surface, or ii) K^2_S=3, the bicanonical map is a degree two morphism and Z is birational to an Enriques surface. Up to now no example of case ii) was known. Here an explicit construction of all such surfaces is given. Furthermore it is shown that the corresponding subset of the moduli space of surfaces of general type is irreducible and uniruled of dimension 6.

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