Nagata Conjecture Linear Series Seshadri Constants Harbourne-Hirschowitz Conjecture Big Divisors
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 405p-430p
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