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Classification of
singular ℚ-homology planes, II:
ℂ1- and ℂ∗-rulings
Karol Palka |
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Vol. 258 (2012), No. 2, 421–457
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Abstract |
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A ℚ-homology plane is a normal complex algebraic surface having trivial rational homology. We classify singular ℚ-homology planes that are ℂ1- or ℂ∗-ruled. We analyze their completions, the number of different rulings they have, and the number of affine lines on them; and we give constructions. Together with previously known results, this completes the classification of ℚ-homology planes with smooth locus of nongeneral type. We show also that the dimension of a family of homeomorphic but nonisomorphic singular ℚ-homology planes having the same weighted boundary, singularities and Kodaira dimension can be arbitrarily big. |
Keywords
acyclic surface, homology plane, ℚ-homology plane
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Mathematical Subject Classification 2010
Primary: 14R05
Secondary: 14J17, 14J26
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Milestones
Received: 11 May 2011
Revised: 14 September 2011
Accepted: 27 September 2011
Published: 1 August 2012
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Authors |
| Karol Palka | |
| Institute of Mathematics University of Warsaw Ul. Banacha 2 02-097 Warsaw Poland |
Institute of Mathematics Polish Academy of Sciences ul. Śniadeckich 8 00-956 Warsaw Poland |
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