Mercredi 13 novembre, Salle Duhem, M3
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
two-dimensional cyclic quotient singularity.
This is a joint work with Mohan Bhupal.
Résumé Let K be an algebraically closed field and let X
subset K^m be an n-dimensional 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 well-known 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.