Surfaces of general type with p g =0, K 2=6 and non birational bicanonical map

Abstract

Let S be a minimal surface of general type with pg=0 and K2=6, such that its bicanonical map Open image in new window is not birational. The map φ is a morphism of degree ≤ 4 onto a surface. The case of degφ = 4 is completely classified in [Topology, 40 (5) (2001), 977–991] and the present paper completes the characterization of these surfaces. It is proven that the degree of φ cannot be equal to 3, and the geometry of surfaces with degφ = 2 is analysed in detail. The last section contains three examples of such surfaces, two of which appear to be new.