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.