The classification of surfaces with p_g=0, K²=6 and non birational bicanonical map

2003/01/13 by Lopes, Margarida Mendes, Pardini, Rita
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0301138

Abstract

Let S be a minimal surface of general type with p_g=0 and K²=6, such that its bicanonical map \fie\colon S→\pp⁶ is not birational. The map \fie is a morphism of degree ≤ 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.

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