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

Abstract

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 $°\fie=4$ 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 $°\fie=2$ is analysed in detail. The last section contains three examples of such surfaces, two of which appear to be new.

arXiv commentLatex, 18 pages Minor correction in the proof of Lemma 2.1

References in corpus (1)

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