A connected component of the moduli space of surfaces of general type with $p_g=0$

Details A connected component of the moduli space of surfaces of general type with $p_g=0$ A connected component of the moduli space of surfaces of general type with $p_g=0$

1999-10-04

arxiv.org/abs/math/9910012v1

Mathematics

Algebraic Geometry

LaTeX 2.09, 20 pages

Scientific paper

Let S be a minimal surface of general type with $p_g(S)=0$ and such that the bicanonical map $\phi:S\to \pp^{K^2_S}$ is a morphism: then the degree of $\phi$ is at most 4 and if it is equal to 4 then $K^2_S\le 6$. Here we prove that if $K^2_S=6$ and $\deg \phi=4$ then S is a so-called {\em Burniat surface}. In addition we show that minimal surfaces with $p_g=0$, $K^2=6$ and bicanonical map of degree 4 form a 4-dimensional irreducible connected component of the moduli space of surfaces of general type.

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