Let be a closed real-analytic subset and putThis article deals with the question of the structure of . In the main result a natural proof is given for the fact, that always is closed. As a main tool an interesting relation between complex analytic subsets of of positive dimension and the Segre varieties of is proved and exploited.
The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings of S which might...
Soit un espace analytique projectif et un faisceau cohérent sur . On construit des recouvrements de formés d’intérieurs de compacts dont toutes les intersections sont -privilégiées, en un sens convenable. On utilise de tels recouvrements pour donner une nouvelle démonstration du théorème de semi-continuité pour un morphisme projectif.
We deal with a reduction of power series convergent in a polydisc with respect to a Gröbner basis of a polynomial ideal. The results are applied to proving that a Nash function whose graph is algebraic in a "large enough" polydisc, must be a polynomial. Moreover, we give an effective method for finding this polydisc.
Existence of loops for non-injective regular analytic transformations of the real plane is shown. As an application, a criterion for injectivity of a regular analytic transformation of in terms of the Jacobian and the first and second order partial derivatives is obtained. This criterion is new even in the special case of polynomial transformations.
We prove a theorem on the boundary regularity of a purely p-dimensional complex subvariety of a relatively compact, strictly pseudoconvex domain in a Stein manifold. Some applications describing the structure of the polynomial hull of closed curves in Cn are also given.
This article continues the investigation of the analytic intersection algorithm from the perspective of deformation to the normal cone, carried out in the previous papers of the author [7, 8, 9]. The main theorem asserts that, given an analytic set V and a linear subspace S, every collection of hyperplanes, admissible with respect to an algebraic bicone B, realizes the generalized intersection index of V and S. This result is important because the conditions for a collection of hyperplanes to be...
We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.
Our objective is to construct residue currents from Bochner-Martinelli type kernels; the computations hold in the non complete intersection case and provide a new and more direct approach of the residue of Coleff-Herrera in the complete intersection case; computations involve crucial relations with toroidal varieties and multivariate integrals of the Mellin-Barnes type.