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.
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