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Séminaire étudiants : An introduction to the Cayley-Bacharach theorems

Mercredi 15 novembre 14:15-15:15 - Rémi Bignalet - Université de Bourgogne

Séminaire étudiants : An introduction to the Cayley-Bacharach theorems

Résumé : Following the article Cayley-Bacharach theorems and conjectures by D.Eisenbud, M.Green and J.Harris, I will explain the evolution of a series of geometrical results beginning in the fourth century a.d. and known as Cayley-Bacharach theorems. One of this statement establish that if one takes two cubics in the complex projective planes meeting in nine distinct points p1 , . . . , p9 , then any other cubic containing eight of the nine points, for example p1 , . . . , p8, contains necessarily the ninth point p9 (Chasles’ theorem, XIXth century). After explaining the previous versions of this result and some tools necessary to understand it, I will state the more recent versions using the notion of Gorenstein ring and I’ll give some concrete examples to show the interest of such a generalization.

Lieu : A318

Pour en savoir plus sur cet événement, consultez l'article Séminaire étudiants