Univ Lille 1

Journée "Lille-Bucuresti"
organisée par le séminaire Singularités et Applications

                                        Coordonnateur : Mihai Tibar

Mardi 25 mai, Salle Duhem, M3
14:00-14:45 Chen Ying  
  Polynômes mixtes et polyèdre de Newton
Résumé On discute une généralisation dans le cas réel analytique d'un théorème de A. Némethi et A. Zaharia.

Pause café     
15:00-15:45 Mihai Tibar  
Déformations des polynômes et nombres de Betti
Vers une classification des polynômes avec le nombre de Betti de plus haut rang proche du maximum.
16:00-16:50 Cezar Joita (Bucuresti)  
  Cohomological q-convexity in top degrees for Zariski open sets in P^n
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 $H^{n-2}(\mathbb{P}^n\setminus A,{\cal F})=0$.
Pause café    
17:10-18:00 Mihnea Coltoiu (Bucuresti)  
  On the disk theorem 
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.