On the existence of plane curves with prescribed multiple points
Algebraic Geometry
2007-05-23 v2
Abstract
We address the problem of determining the degree a plane curve must have in order to pass with multiplicity m through r points in general position. A conjecture of Nagata states that one must have d > m \sqrt{r}. We prove the inequalities d \geq m(r-1)\prod_{i=2}^{r-1}(1-i/(i^2+r-1)) and d > m (\sqrt{r-1} - \pi/8).
Keywords
Cite
@article{arxiv.math/9807066,
title = {On the existence of plane curves with prescribed multiple points},
author = {Joaquim Roe},
journal= {arXiv preprint arXiv:math/9807066},
year = {2007}
}
Comments
13 pages, Latex, XYpic. Revised version, to appear in Journal of Pure and Applied Algebra