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Intégration motivique sur les schémas formels

Julien Sebag (2004)

Bulletin de la Société Mathématique de France

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.

Is the Luna stratification intrinsic?

Jochen Kuttler, Zinovy Reichstein (2008)

Annales de l’institut Fourier

Let G GL ( V ) be a representation of a reductive linear algebraic group G on a finite-dimensional vector space V , defined over an algebraically closed field of characteristic zero. The categorical quotient X = V // G carries a natural stratification, due to D. Luna. This paper addresses the following questions:(i) Is the Luna stratification of X intrinsic? That is, does every automorphism of V // G map each stratum to another stratum?(ii) Are the individual Luna strata in X intrinsic? That is, does every automorphism...

Jet schemes of complex plane branches and equisingularity

Hussein Mourtada (2011)

Annales de l’institut Fourier

For m , we determine the irreducible components of the m - th Jet Scheme of a complex branch C and we give formulas for their number N ( m ) and for their codimensions, in terms of m and the generators of the semigroup of C . This structure of the Jet Schemes determines and is determined by the topological type of C .

Killing divisor classes by algebraisation

Alexandru Buium (1985)

Annales de l'institut Fourier

It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.

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