Recent progress in the geometry of Q-acyclic surfaces
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
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arXiv subjects
Karol Palka
Publications and source records attributed to Karol Palka.
Exceptional singular Q-homology planes
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.
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