# Event Calendar

## On the degree of hypersurfaces with given singularities.

Mathematics Colloquium | Michel Waldschmidt | Mar 3rd, 2023

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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 limit $\\Omega(S)$ 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.