# Remarks on the Nagata Conjecture

Strycharz-Szemberg, Beata; Szemberg, Tomasz

Serdica Mathematical Journal (2004)

- Volume: 30, Issue: 2-3, page 405-430
- ISSN: 1310-6600

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topStrycharz-Szemberg, Beata, and Szemberg, Tomasz. "Remarks on the Nagata Conjecture." Serdica Mathematical Journal 30.2-3 (2004): 405-430. <http://eudml.org/doc/219570>.

@article{Strycharz2004,

abstract = {2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.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.},

author = {Strycharz-Szemberg, Beata, Szemberg, Tomasz},

journal = {Serdica Mathematical Journal},

keywords = {Nagata Conjecture; Linear Series; Seshadri Constants; Harbourne-Hirschowitz Conjecture; Big Divisors; linear series; Seshadri constants; Harbourne-Hirschowitz conjecture; big divisors},

language = {eng},

number = {2-3},

pages = {405-430},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Remarks on the Nagata Conjecture},

url = {http://eudml.org/doc/219570},

volume = {30},

year = {2004},

}

TY - JOUR

AU - Strycharz-Szemberg, Beata

AU - Szemberg, Tomasz

TI - Remarks on the Nagata Conjecture

JO - Serdica Mathematical Journal

PY - 2004

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 30

IS - 2-3

SP - 405

EP - 430

AB - 2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.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.

LA - eng

KW - Nagata Conjecture; Linear Series; Seshadri Constants; Harbourne-Hirschowitz Conjecture; Big Divisors; linear series; Seshadri constants; Harbourne-Hirschowitz conjecture; big divisors

UR - http://eudml.org/doc/219570

ER -

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