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

Abstract

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.

32 pages, to appear in Pacific J.M

References in corpus (1)

• Classification of weighted graphs up to blowing-up and blowing-down

Cited by in corpus (2)

• Classification of planar rational cuspidal curves. I. C**-fibrations
• A Note on Rational Cuspidal curves on $\mathbb{Q}$-Homology Projective Planes