Effectiveness - non effectiveness in semialgebraic and PL geometry.
Ein Semialgebraischer Beweis der Topologischen Form des Hauptsatzes von zariski.
Eine Bemerkung zu den höheren Pythagoraszahlen reeller Körper.
Embedding of real varieties and their subvarieties into Grassmannians.
Given a compact affine nonsingular real algebraic variety X and a nonsingular subvariety Z C X belonging to a large class of subvarieties, we show how to embed X in a suitable Grassmannian so that Z becomes the transverse intersection of the zeros of a section of the tautological bundle on the Grassmannian.
Embedding Semi-Algebraic Spaces.
Ensembles semi-algébriques symétriques par arcs.
Entropy, homology and semialgebraic geometry
Enumeration of real conics and maximal configurations
We use floor decompositions of tropical curves to prove that any enumerative problem concerning conics passing through projective-linear subspaces in is maximal. That is, there exist generic configurations of real linear spaces such that all complex conics passing through these constraints are actually real.
Equidistribution of Frobenius classes and the volumes of tubes
Équisingularité réelle II : invariants locaux et conditions de régularité
On définit, pour un germe d’ensemble sous-analytique, deux nouvelles suites finies d’invariants numériques. La première a pour termes les localisations des courbures de Lipschitz-Killing classiques, la seconde est l’équivalent réel des caractéristiques évanescentes complexes introduites par M. Kashiwara. On montre que chaque terme d’une de ces suites est combinaison linéaire des termes de l’autre, puis on relie ces invariants à la géométrie des discriminants des projections du germe sur des plans...
Equivalence of analytic and rational functions
We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.
Equivariant virtual Betti numbers
We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincaré series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of , and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.
Ergänzung zur Arbeit "Quadratische Formen über affinen Algebren und ein algebraischer Beweis des Satzes von Borsuk-Ulam".
Erratum to : Morphisms, line bundles and moduli spaces in real algebraic geometry
Espace des germes d'arcs réels et série de Poincaré d'un ensemble semi-algébrique
Nous définissons l’espace des germes d’arcs réels tracés sur un ensemble semi-algébrique de , analogue réel de la théorie développée par Denef et Loeser concernant l’espace des germes d’arcs tracés sur une variété algébrique complexe. Puis, reprenant leur méthodes, nous prouvons la rationalité de la série de Poincaré associée à un ensemble semi-algébrique.
Even Symmetric Sextics.
Every connected sum of lens spaces is a real component of a uniruled algebraic variety
We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.
Every finitely presented group is the ...of some two dimensional Stein space.
Examples of functions -extendable for each finite, but not -extendable
In Example 1, we describe a subset X of the plane and a function on X which has a -extension to the whole for each finite, but has no -extension to . In Example 2, we construct a similar example of a subanalytic subset of ; much more sophisticated than the first one. The dimensions given here are smallest possible.
Existence of flat tori in analytic manifolds of nonpositive curvature