Frameworks for two-dimensional Keller maps

Abstract

A Keller map is a counterexample to the Jacobian Conjecture. In dimension two every such map, if exists, leads to a complicated set of conditions on the map between the Picard groups of suitable compactifications of the affine plane. This is essentially a combinatorial problem. Several solutions to it ("frameworks") are described in detail. Each framework corresponds to a large system of equations, whose solution would lead to a Keller map.