%0 Journal Article
%T A geometric approach to the two-dimensional Jacobian Conjecture
%A Alexander Borisov
%J Mathematics
%D 2009
%I arXiv
%X Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is obtained by resolving this map. Several structural results are proven, revealing a rather orderly structure of the graph of the curves at infinity. We also exhibit and discuss a graph that may lead to a counterexample to the Jacobian Conjecture.
%U http://arxiv.org/abs/0912.4803v1