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arXiv · 0912.4803

A geometric approach to the two-dimensional Jacobian Conjecture

Alexander Borisov
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Abstract

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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Alexander Borisov. 2009-12-24. A geometric approach to the two-dimensional Jacobian Conjecture. https://arxiv.org/abs/0912.4803

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