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

M. Mendes Lopes; R. Pardini

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arXiv · math/9910012

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

M. Mendes Lopes·R. Pardini

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Abstract

Let S be a minimal surface of general type with $p_g(S)=0$ and such that the bicanonical map $ϕ:S\to \pp^{K^2_S}$ is a morphism: then the degree of $ϕ$ 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 $°ϕ=4$ 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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BibTeX RIS

M. Mendes Lopes, R. Pardini. 1999-10-04. A connected component of the moduli space of surfaces of general type with $p_g=0$. https://arxiv.org/abs/math/9910012

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