Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1746

 Title: Remarks on the Nagata Conjecture Authors: Strycharz-Szemberg, BeataSzemberg, Tomasz Keywords: Nagata ConjectureLinear SeriesSeshadri ConstantsHarbourne-Hirschowitz ConjectureBig Divisors Issue Date: 2004 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 405p-430p Abstract: The famous Nagata Conjecture predicts the lowest degree of a plane curve passing with prescribed multiplicities through given points in general position. We explain how this conjecture extends naturally via multiple point Seshadri constants to ample line bundles on arbitrary surfaces. We show that if there exist curves of unpredictable low degree, then they must have equal multiplicities in all but possibly one of the given points. We use this restriction in order to obtain lower bounds on multiple point Seshadri constants on a surface. We discuss also briefly a seemingly new point of view on the Nagata Conjecture via the bigness of the involved linear series. Description: 2000 Mathematics Subject Classification: 14C20, 14E25, 14J26. URI: http://hdl.handle.net/10525/1746 ISSN: 1310-6600 Appears in Collections: Volume 30 Number 2-3

Files in This Item:

File Description SizeFormat