Coordonnateur : Mihai Tibar
Mardi 25 mai, Salle Duhem, M3
Résumé On discute une généralisation dans le cas réel analytique d'un théorème de A. Némethi et A. Zaharia.
Résumé Vers une classification des polynômes avec le nombre de Betti de plus haut rang proche du maximum.
Abstract. We show that if A is a closed analytic subset of P^n of pure codimension q then $H^i(\mathbb{P}^n\setminus A,{\cal F})$ are finite dimensional for every coherent algebraic sheaf ${\cal F}$ and every $i\geq n-\left[\frac{n-1}{q}\right]$. If $n-1\geq 2q$ we show that $H^{n-2}(\mathbb{P}^n\setminus A,{\cal F})=0$.
Abstract. We construct an example of a 2 dimensional Stein normal space X with one singular point $x_0$ such that $X \setminus \{x_0\}$ is simply connected and it satisfies the disk condition. This answers a question raised by Fornaess and Narasimhan. We also prove that any increasing union of Stein open sets contained in a Stein space of dimension 2 satisfies the disk condition. Starting from the above example we exhibit, without using deformation theory, a new type of 2 dimensional holes which cannot be filled.