Remarks on the Nagata Conjecture

Strycharz-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 -