Tomasz Szemberg

Title:  Waldschmidt constants

Abstract: 

Bombieri in his proof of Schwarz Lemma in Complex Analysis introduced
an invariant associated with symbolic powers of an ideal of functions
vanishing at a finite set of points. This invariant measures in effect the
asymptotic ratio of the least degree of a polynomial in several variables
vanishing in the given finite set of points to the order of vanishing in
these points. This invariant has been studied by Waldschmidt, Skoda,
Demailly, Esnault and Viehweg. It is not clear weather it was Dumnicki
or Harbourne who introduced the name Waldschmidt constant.
These constants are very hard to compute in general. A number of
conjectures in the theory of linear systems on projective spaces can
be stated in the language of Waldschmidt constants, including the
Nagata Conjecture and its various generalizations.
I will report on cases when Waldschmidt constants are known, or where
there is an algorithmic procedure to compute them available. This includes
square free monomial ideals and ideals of singular points of certain
line point configurations.