English

A geometric approach to the two-dimensional Jacobian Conjecture

Algebraic Geometry 2009-12-25 v1

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.

Keywords

Cite

@article{arxiv.0912.4803,
  title  = {A geometric approach to the two-dimensional Jacobian Conjecture},
  author = {Alexander Borisov},
  journal= {arXiv preprint arXiv:0912.4803},
  year   = {2009}
}

Comments

17 pages, 1 figure

R2 v1 2026-06-21T14:28:05.801Z