On Resolution of Compactifications of Unramified Planar Self-maps
Algebraic Geometry
2012-04-12 v4
Abstract
We use the techniques of birational algebraic geometry and some combinatorial arguments related to weighted trees to study the structure of resolutions of compactifications of hypothetical counterexamples to the two-dimensional Jacobian Conjecture. We obtain especially detailed results for the Stein decomposition of such maps. We hope that our approach will inspire more birational geometers to seriously work on the Jacobian Conjecture.
Keywords
Cite
@article{arxiv.1110.5118,
title = {On Resolution of Compactifications of Unramified Planar Self-maps},
author = {Alexander Borisov},
journal= {arXiv preprint arXiv:1110.5118},
year = {2012}
}
Comments
This is a major revision. The proof of the result of Domrina is rescinded due to a mistake. The paper is significantly expanded to include a number of new results and methods, including the determinants of weighted trees as well as some relevant adjunction and inversion of adjunction