On the Intersection of Two Plane Curves
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- March 2000
- DOI:
- 10.48550/arXiv.math/0003063
- arXiv:
- arXiv:math/0003063
- Bibcode:
- 2000math......3063C
- Keywords:
-
- Algebraic Geometry;
- 14H10;
- 32Q45
- E-Print:
- 13 pages in AMS-LATEX. To appear on MRL