14 may 2014 -- 16:00
Sala Seminari (DM, Pisa)
Seminari di Geometria
Abstract.
In this seminar we present the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X in Rn, 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.