2009/12/24 by Borisov, Alexander
#14E05 #14E30 #14J26 #14R15 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0912.4803
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.