Classification of singular Q-homology planes. II. C^1- and C*-rulings

Details Classification of singular Q-homology planes. II. C^1- and C*-rulings Classification of singular Q-homology planes. II. C^1- and C*-rulings

2012-01-12

arxiv.org/abs/1201.2463v1

Mathematics

Algebraic Geometry

32 pages, to appear in Pacific J.M

Scientific paper

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular Q-homology planes which are C^1- or C*-ruled. We analyze their completions, the number of different rulings, the number of affine lines on it and we give constructions. Together with previously known results this completes the classification of Q-homology planes with smooth locus of non-general type. We show also that the dimension of a family of homeomorphic but non-isomorphic singular Q-homology planes having the same weighted boundary, singularities and Kodaira dimension can be arbitrarily big.

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