On Nagata's Conjecture
Abstract
Modifying an approach of J. Roe, this paper gives an improved lower bound on the degrees d such that for general points p1,...,pn in P2 and m > 0 there is a plane curve of degree d vanishing at each point pi with multiplicity at least m. In certain cases, for m not too large compared with n, the new bound implies a bound conjectured by Nagata.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 1999
 arXiv:
 arXiv:math/9909093
 Bibcode:
 1999math......9093H
 Keywords:

 Algebraic Geometry;
 14N99
 EPrint:
 6 pages