Intégrales asymptotiques et monodromie
Nous généralisons la théorie de l’intégration motivique au cadre des schémas formels. Nous définissons et étudions l’anneau booléen des ensembles mesurables, la mesure motivique, l’intégrale motivique et nous démontrons un théorème de changement de variables pour cette intégrale.
Let be a representation of a reductive linear algebraic group on a finite-dimensional vector space , defined over an algebraically closed field of characteristic zero. The categorical quotient carries a natural stratification, due to D. Luna. This paper addresses the following questions:(i) Is the Luna stratification of intrinsic? That is, does every automorphism of map each stratum to another stratum?(ii) Are the individual Luna strata in intrinsic? That is, does every automorphism...
For , we determine the irreducible components of the th Jet Scheme of a complex branch and we give formulas for their number and for their codimensions, in terms of and the generators of the semigroup of . This structure of the Jet Schemes determines and is determined by the topological type of .
It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.
La condition “ constant” est une condition numérique d’équisingularité introduite par B. Teissier. Celui-ci a démontré dans (Astérisque, 7 & 8 (1973) II. Théorème 3.9) que cette condition implique les conditions de Whitney, nous montrons ici la réciproque.
Let denote the set of log canonical thresholds of pairs , with a nonsingular variety of dimension , and a nonempty closed subscheme of . Using non-standard methods, we show that every limit of a decreasing sequence in lies in , proving in this setting a conjecture of Kollár. We also show that is closed in ; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in order to check...