"Two invariants related to two conjectures due to Nagata"

by Prof. Michel Waldschmidt (Institut de Mathematiques de Jussieu, France)

Thursday, December 14, 2017 from 16:00 to 17:00 (Asia/Kolkata)
at TIFR, Mumbai ( AG-69 )

Description

Abstract:

Seshadri's constant is related to a conjecture due to Nagata. Another
conjecture, also due to Nagata and solved by Bombieri in 1970, is related
with algebraic values of meromorphic functions. The main part of
Bombieri's proof leads to a Schwarz Lemma in several variables, the proof
of which gives rise to another invariant associated with symbolic powers
of the ideal of functions vanishing on a finite set of points. This
invariant is an asymptotic measure of the least degree of a polynomial in
several variables with given order of vanishing on a finite set of points.
Recent works on the resurgence of ideals of points and the containment
problem compare powers and symbolic powers of ideals.