A geometric approach to the two-dimensional Jacobian Conjecture

Details A geometric approach to the two-dimensional Jacobian Conjecture A geometric approach to the two-dimensional Jacobian Conjecture

2009-12-24

arxiv.org/abs/0912.4803v1

Mathematics

Algebraic Geometry

17 pages, 1 figure

Scientific paper

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.

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