Buondì,

vi segnalo il seminario di geometria di questa settimana, sempre mercoledì in aula seminari alle 16. a presto, Bruno

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MERCOLEDI' 14 MAGGIO 2014

SEMINARI DI GEOMETRIA 16:00-17:00, Sala Seminari (Dip. Matematica) On the Nullstellensätze for Stein spaces and C-analytic sets Jose Fernando (Universidad Computense, Madrid)

Abstract: In this seminar we present the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X in R^n, in terms of the saturation of Lojasiewicz's radical in O(X):

the ideal I(Z(a)) of all functions vanishing on the zero-set Z(a) of an ideal a of O(X) coincides with the saturation of Lojasiewicz's radical of a.

If Z(a} has `good properties' concerning Hilbert's 17th Problem, then I(Z(a} is the closure of the real radical of a.

The same holds if we replace the real radical with the real-analytic radical, which is a natural generalization of the real radical ideal in the C-analytic setting.

(joint with Francesca Acquistapace and Fabrizio Broglia)

We also revisit the classical results concerning (Hilbert's) Nullstellensatz in the framework of (complex) Stein spaces.