Date 16 November at 4 pm.
Speaker: Michel Waldschmidt, University of Sorbonne, Paris
Title
On the degree of hypersurfaces with given singularities
Abstract
Let $n$, $t$ be positive integers and $S$ be a finite set of points in
$\C^n$. We denote by $\omega_t(S)$ the least degree of a nonzero polynomial
vanishing with multiplicity at least $t$ at each point of $S$. The sequence
$(\omega_t(S)/t)_{t\ge 0}$ has a limite $\Omega(S)$ as $t$ tends to
infinity. This invariant was introduced in 1975 for the proof of a Schwarz
Lemma in several variables which occurs in the solution by Bombieri in 1970
of a conjecture of Nagata dealing with a generalization of a transcendence
result of Schneider and Lang. The same invariant occurs in connection with
another conjecture that Nagata introduced in 1959 in his work on Hilbert's
14th problem. It is closely related with Seshadri's constant.