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

TL;DR

This paper classifies singular Q-homology planes that are C^1- or C*-ruled, analyzing their structures, rulings, and affine lines, and explores the diversity of such planes with identical invariants.

Contribution

It provides a complete classification of singular Q-homology planes with specific rulings and analyzes their moduli, extending previous results.

Findings

Classification of singular Q-homology planes with C^1- or C*-rulings.

Analysis of their completions and rulings.

Construction of examples with arbitrarily large families of non-isomorphic planes.

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.