Lucja Farnik

Title: Asymptotic Hilbert polynomial and Waldschmidt constants

Abstract: 
The famous Nagata conjecture can be expressed in the following way: in the 
projective plane the Waldschmidt constant for an ideal of r>9 points in very 
general position is equal to sqrt(r). The Waldschmidt constant is the asymptotic 
counterpart of the initial degree of an ideal. Computing this constant is an 
open question in general, it is even difficult to compute the initial degree 
of a symbolic power of an ideal. I will discuss some classical bounds for 
the Waldschmidt constants and show an upper bound in terms of the asymptotic 
Hilbert polynomial. This is a joint work with M. Dumnicki and H. Tutaj-Gasinska.