Surfaces with $p_g = 0$, $K^2 = 5$ and bicanonical maps of degree 4

Details Surfaces with $p_g = 0$, $K^2 = 5$ and bicanonical maps of degree 4 Surfaces with $p_g = 0$, $K^2 = 5$ and bicanonical maps of degree 4

2010-11-04

arxiv.org/abs/1011.1061v1

Mathematics

Algebraic Geometry

35pages

Scientific paper

Let $S$ be a minimal surface of general type with $p_g(S) = 0, K_S^2 = 5$ and
bicanonical map of degree 4. Denote by $\Sigma$ the bicanonical image. If
$\Sigma$ is smooth, then $S$ is a Burniat surface; and if $\Sigma$ is singular,
then we reduced $\Sigma$ to one case and described it, furthermore $S$ has at
most one $(-2)$-curve.

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