On the nullstellensätze for stein spaces and C-analytic sets.

In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ⊂ Rn in terms of the saturation of Łojasiewicz’s radical in O(X): The ideal I(Ƶ(a)) of the zero-set Ƶ(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of Łojasiewicz’s radical (Formula presented). If Ƶ(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(Ƶ(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(Ƶ(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of Ƶ(p).

"Le ravissementde Lol. V. Stein" se mira en "Moderato cantabile": algunos ecos narrativos en la escritura de Marguerite Duras

El artículo presenta la novela "Moderato cantabile" como texto fundador del universo narrativo de Marguerite Duras al contener y avanzar los temas principales y las estructuras discursivas esenciales del mismo. A partir de esta perspectiva de lectura, confrontaremos "Moderato cantabile" con la novela publicada en 1964, "Le ravissement de Lol. V. Stein", lo que permite plantear un juego de espejos entre ambos relatos, del que resultan las claves interpretativas para comprender los textos de la autora.