Affine Algebraic Geometry

Abstract

Affine geometry deals with algebro-geometric questions of affine varieties that are treated with methods coming from various areas of mathematics like commutative and non-commutative algebra, algebraic, complex analytic and differential geometry, singularity theory and topology. The conference had several main topics. One of them was the famous Jacobian problem, its connections with the Dixmier conjecture and possible algebraic approaches and reductions. A second main theme were questions on Log algebraic varieties, in particular log algebraic surfaces. Thirdly, results on automorphisms of An played a major role, in particular the solution of the Nagata problem, actions of algebraic groups on An , Hilbert’s 14th problem and locally nilpotent derivations. More generally automorphism groups of affine and non-affine varieties, especially in dimension 2 and 3 were treated, and substantial progress on the cancelation problem and embedding problem was presented.