Affine lines on affine surfaces and the Makar Limanov Invariant
by
Peter Russell
Dpartement of Mathematics, McGill University
Coauthors: R. Gurjar, K. Masuda, M. Miyanishi

I will report on joint work with R. Gurjar, K. Masuda and M. Miyanishi on surfaces S with the MLi property. (A smooth affine surface is MLi if the Makar-Limanov invariant, the intersection taken over all additive actions of their rings of invariants, has dimension i.) We investigate the existence of open subsets isomorphic to the affine plane on such surfaces and, generalizing the Abyankar-Moh-Suzuki theorem, we settle the question whether an affine line on S is always a fiber component of a fibration of S by affine lines for ML0 surfaces whose Picard group is torsion and for ML1 surfaces. We also investigate the ascent and descent of the MLi property under proper maps.

Date received: March 30, 2005