Exceptional singular Q-homology planes

Details Exceptional singular Q-homology planes Exceptional singular Q-homology planes

2009-09-04

arxiv.org/abs/0909.0772v2

Mathematics

Algebraic Geometry

19 pages, 8 figures

Scientific paper

We consider singular Q-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is C^1- or C*-ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type A1 and A2 respectively. These surfaces can be constructed starting from two classical configurations of lines on the projective plane: the dual Hesse configuration and the complete quadrangle.

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