Exceptional singular Q-homology planes

Abstract

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.

19 pages, 8 figures

References in corpus (3)

• Abstract configurations in algebraic geometry
• The Hesse pencil of plane cubic curves
• Recent progress in the geometry of Q-acyclic surfaces

Cited by in corpus (11)

• The Coolidge-Nagata conjecture
• Cuspidal curves, minimal models and Zaidenberg's finiteness conjecture
• The Coolidge-Nagata conjecture, part I
• Classification of singular Q-homology planes. II. C^1- and C*-rulings
• Recent progress in the geometry of Q-acyclic surfaces
• A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-Suzuki
• Classification of singular Q-homology planes. I. Structure and singularities
• The geometry of sporadic ${\mathbb{C}}^{\ast }$-embeddings into ${\mathbb{C}}^2$
• Singular Q-homology planes of negative Kodaira dimension have smooth locus of non-general type
• The Coolidge-Nagata conjecture holds for curves with more than four cusps
• A Note on Rational Cuspidal curves on $\mathbb{Q}$-Homology Projective Planes