On the Intersection of Two Plane Curves
Algebraic Geometry
2007-05-23 v2
Abstract
We study the following question: fix a sufficient general curve D of degree d in P^2, what is the least number of intersections between D and an irreducible curve of degree m? G. Xu proved this number i(d, m) is at least d - 2 for all m. This problem can be regarded as the algebraic part of Kobayashi conjecture on the hyperbolicity of P^2 D. We first improved Xu's bound with m fixed and then generalized his result to rational ruled surfaces.
Cite
@article{arxiv.math/0003063,
title = {On the Intersection of Two Plane Curves},
author = {Xi Chen},
journal= {arXiv preprint arXiv:math/0003063},
year = {2007}
}
Comments
13 pages in AMS-LATEX. To appear on MRL