Illinois Journal of Mathematics

Linear systems of plane curves with imposed multiple points

Joaquim Roé

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Abstract

A conjecture of Harbourne and Hirschowitz implies that $r \ge 9$ general points of multiplicity $m$ impose independent conditions to the linear system of curves of degree $d$ when $d(d+3) \ge rm(m+1)-2$. In this paper we prove that the conditions are independent provided $d+2\ge (m+1)(\sqrt{r+1.9}+\pi /8) $.

Article information

Source
Illinois J. Math., Volume 45, Number 3 (2001), 895-906.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138158

Digital Object Identifier
doi:10.1215/ijm/1258138158

Mathematical Reviews number (MathSciNet)
MR1879242

Zentralblatt MATH identifier
0988.14002

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14H20: Singularities, local rings [See also 13Hxx, 14B05] 14H50: Plane and space curves

Citation

Roé, Joaquim. Linear systems of plane curves with imposed multiple points. Illinois J. Math. 45 (2001), no. 3, 895--906. doi:10.1215/ijm/1258138158. https://projecteuclid.org/euclid.ijm/1258138158


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