Classification of singular Q-homology planes. I. Structure and singularities

Details Classification of singular Q-homology planes. I. Structure and singularities Classification of singular Q-homology planes. I. Structure and singularities

2008-06-19

arxiv.org/abs/0806.3110v4

Mathematics

Algebraic Geometry

improved results from Ph.D. thesis (University of Warsaw, 2009), 25 pages, to appear in Israel J. Math

Scientific paper

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient singularity then it is a quotient of an affine cone over a projective curve by an action of a finite group respecting the set of lines through the vertex. In particular, it is contractible, has negative Kodaira dimension and only one singular point. We describe minimal normal completions of such planes.

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