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On the degree of hypersurfaces with given singularities.

Mathematics Colloquium | Michel Waldschmidt | Mar 3rd, 2023

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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.

About the Speaker:

Michel Waldschmidt is Professor Emeritus at Sorbonne University, Paris. His main field is  Number theory.  According to the Mathematics Genealogy Project, he has 23 students and 135 descendants. He received the Prix Peccot of the College de France in 1977, the Médaille d’Argent du CNRS in 1978,  the Distinguished Award of the Hardy-Ramanujan Society in 1986, The AMS Bertrand Russell Prize in 2021; he is Doctor Honoris Causa from Ottawa University. In 2013, he has been President of the Société Mathématique de France, Vice President of the Centre International de Mathématiques Pures et Appliquées (CIMPA), Chair of the Committee for Developing Countries of the European Mathematical Society. He has been a member of the Commission for Developing Countries of the International Mathematical Union until 2022. 

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