On the Intersection of Two Plane Curves

2000/03/10 by Xi Chen, Chen, Xi
Mathematics · #14H10 #32Q45 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10 #msc:32Q45

paper · pdf · doi:10.48550/arxiv.math/0003063

13 pages in AMS-LATEX. To appear on MRL

arxiv created 2000/09/15 · arxiv updated 2009/11/30

Abstract

We study the following question: fix a sufficient general curve D of degree d in P², 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 P² D. We first improved Xu's bound with m fixed and then generalized his result to rational ruled surfaces.

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