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Title: Remarks on the Nagata Conjecture
Authors: Strycharz-Szemberg, Beata
Szemberg, Tomasz
Keywords: Nagata Conjecture
Linear Series
Seshadri Constants
Harbourne-Hirschowitz Conjecture
Big 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.
ISSN: 1310-6600
Appears in Collections:Volume 30 Number 2-3

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