Equidimensionality of the Brauer loop scheme.
Équidistribution des sous-variétés de petite hauteur
On montre dans cet article que le théorème d’équidistribution de Szpiro-Ullmo-Zhang concernant les suites de petits points sur les variétés abéliennes s’étend au cas des suites de sous-variétés. On donne également une version quantitative de ce résultat.
Equidistribution of dynamically small subvarieties over the function field of a curve
Equidistribution of Frobenius classes and the volumes of tubes
Equidistribution of small subvarieties of an Abelian variety.
Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero
2000 Mathematics Subject Classification: 14B05, 32S25.The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution processes, both classical and modern. In this paper we explore how it changes by blowing–up.* Supported by FQM 304 and BFM 2000–1523. ** Supported by FQM 218 and BFM 2001–3207.
Equisingular deformations below the Newton boundary
Equisingular deformations of isolated 2-dimensional hyper-surface singularities.
Equisingular generic discriminants and Whitney conditions
The purpose of this article is to show that the Whitney conditions are satisfied for complex analytic families of normal surface singularities for which the generic discriminants are equisingular. According to J. Briançon and J. P. Speder the constancy of the topological type of a family of surface singularities does not imply Whitney conditions in general. We will see here that for a family of minimal normal surface singularities these two equisingularity conditions are equivalent.
Équisingularité générique des familles de surfaces à singularité isolée
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 classes of Latin squares and nets in
The fundamental combinatorial structure of a net in is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in are empty to show some non-existence results for 4-nets in .
Equivalence classes of the 3rd Grassman space over a 5-dimensional vector space.
Équivalence linéaire des idéaux de polynômes
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.
Equivalence of families of singular schemes on threefolds and on ruled fourfolds.
The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of...
Equivalence problem for minimal rational curves with isotrivial varieties of minimal rational tangents
We formulate the equivalence problem, in the sense of É. Cartan, for families of minimal rational curves on uniruled projective manifolds. An important invariant of this equivalence problem is the variety of minimal rational tangents. We study the case when varieties of minimal rational tangents at general points form an isotrivial family. The main question in this case is for which projective variety , a family of minimal rational curves with -isotrivial varieties of minimal rational tangents...
Equivalences between elliptic curves and real quadratic congruence function fields
In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always, the security...
Equivalences between isolated hypersurface singularities.
Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini