




Mercredi 13 novembre, Salle Duhem, M3 

16:0017:00  Burak Özbağcı (Koç University, Istanbul)  
Symplectic fillings of lens spaces and rational blowdowns Résumé We construct a positive allowable Lefschetz fibration over the diskon any minimal (weak) symplectic filling of the canonical contact structure on a lens space. Using this construction we prove that any minimal symplectic filling of the canonical contact structure on a lens space is obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding complex twodimensional cyclic quotient singularity. This is a joint work with Mohan Bhupal. 

17:1018:10  Zbigniew Jelonek (Banach Institute, Warsaw, Pologne)  

On the effective Nullstellensatz Résumé Let K be an algebraically closed field and let X subset K^m be an ndimensional affine variety. Assume that f_1,...,f_k are polynomials which have no common zeros on X. We estimate the degrees of polynomials A_i in K[X] such that 1= sum_{i=1}^k A_i f_i on X. Our estimate is sharp for k le n and nearly sharp for k > n. Now assume that f_1,...,f_k are polynomials on X. Let I =(f_1,...,f_k) subset K[X] be the ideal generated by f_i. It is wellknown that there is a number e(I) (the Noether exponent) such that sqrt{I}^{e(I)} subset I. We give a sharp estimate of e(I) in terms of n and deg f_i. We also give similar estimates in the projective case.  