Involutions on numerical Campedelli surfaces

Details Involutions on numerical Campedelli surfaces Involutions on numerical Campedelli surfaces

2005-11-15

arxiv.org/abs/math/0511391v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

Numerical Campedelli surfaces are minimal surfaces of general type with p_g=0 (and so q=0) and K^2=2. Although they have been studied by several authors, their complete classification is not known. In this paper we classify numerical Campedelli surfaces with an involution, i.e. an automorphism of order 2. First we show that an involution on a numerical Campedelli surface S has either four or six isolated fixed points, and the bicanonical map of S is composed with the involution if and only if the involution has six isolated fixed points. Then we study in detail each of the possible cases, describing also several examples.

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