Real Algebraic Geometry and the 17th Hilbert Problem.
Real algebraic spaces
Real algebraic structures on topological spaces
Real analytic approximation of locally embeddable CR manifolds
Real analytic manifolds in with parabolic complex tangents along a submanifold of codimension one
We will classify -dimensional real submanifolds in which have a set of parabolic complex tangents of real dimension . All such submanifolds are equivalent under formal biholomorphisms. We will show that the equivalence classes under convergent local biholomorphisms form a moduli space of infinite dimension. We will also show that there exists an -dimensional submanifold in such that its images under biholomorphisms , , are not equivalent to via any local volume-preserving holomorphic...
Real analytic projective planes with large automorphism groups.
Real and complex analytic sets. The relevance of Segre varieties
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.
Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.
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...
Realtive komplexe Quotienten.
Recouvrements privilégiés
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.
Réduction d'albanèse d'un morphisme propre et faiblement kahlérien. II. Groupes d'automorphismes relatifs
Réduction d'albanèse d'un morphisme propre et faiblement kahlérien. I
Reduction of Power Series in a Polydisc with Respect to a Gröbner Basis
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.
Regular analytic arcs and curves
Regular analytic transformations of
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.
Regularity for elliptic pairs over
Regularity of varieties in strictly pseudoconvex domains.
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.
Regularization of currents and entropy
Relativ analytische Räume.
Relativ-analytische Räume und die Kohärenz von Bildgarben.