1. CJM 2008 (vol 60 pp. 109)
|Affine Lines on Affine Surfaces and the Makar--Limanov Invariant |
A smooth affine surface $X$ defined over the complex field $\C$ is an $\ML_0$ surface if the Makar--Limanov invariant $\ML(X)$ is trivial. In this paper we study the topology and geometry of $\ML_0$ surfaces. Of particular interest is the question: Is every curve $C$ in $X$ which is isomorphic to the affine line a fiber component of an $\A^1$-fibration on $X$? We shall show that the answer is affirmative if the Picard number $\rho(X)=0$, but negative in case $\rho(X) \ge 1$. We shall also study the ascent and descent of the $\ML_0$ property under proper maps.
2. CJM 2004 (vol 56 pp. 1145)
|On Log $\mathbb Q$-Homology Planes and Weighted Projective Planes |
We classify normal affine surfaces with trivial Makar-Limanov invariant and finite Picard group of the smooth locus, realizing them as open subsets of weighted projective planes. We also show that such a surface admits, up to conjugacy, one or two $G_a$-actions.
Categories:14R05, 14J26, 14R20