The classification of surfaces with $p_g=0$, $K^2=6$ and non birational bicanonical map

Details The classification of surfaces with $p_g=0$, $K^2=6$ and non birational bicanonical map The classification of surfaces with $p_g=0$, $K^2=6$ and non birational bicanonical map

2003-01-13

arxiv.org/abs/math/0301138v2

Mathematics

Algebraic Geometry

Latex, 18 pages Minor correction in the proof of Lemma 2.1

Scientific paper

Let $S$ be a minimal surface of general type with $p_g=0$ and $K^2=6$, such that its bicanonical map $\fie\colon S\to\pp^6$ is not birational. The map $\fie$ is a morphism of degree $\le 4$ onto a surface. The case of $\deg\fie=4$ is completely characterized in [Topology, {\bf 40} (5) (2001), 977--991] and the present paper completes the classification of these surfaces. It is proven that the degree of $\fie$ cannot be equal to 3, and the geometry of surfaces with $\deg\fie=2$ is analysed in detail. The last section contains three examples of such surfaces, two of which appear to be new.

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