On Moduli of Regular Surfaces with $K^2=8$ $p_g=4$

Paola Supino

Abstract: Let $S$ be a surface of general type with not birational bicanonical map and that does not contain a pencil of genus 2 curves. If $K^2_S=8$, $p_g(S)=4$ and $q(S)=0$ then $S$ can be given as double cover of a quadric surface. We show that its moduli space is generically smooth of dimension $38$, and single out an open subset. Note that for these surfaces $h^2(S,T_S)$ is not zero.

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