Threefolds with nef anticanonical bundles

In this paper we study the global structure of projective threefolds X whose anticanonical bundle K is nef.

Semi-purity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semipurity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

A numerical characterization of hypersurface singularities

In this note we give a numerical characterization of hypersurface singularities in terms of the normalized Hilbert-Samuel coefficients, and we interpret this result from the point of view of rigid polynomials.

Filtrations by complete ideals and applications

Infinitely near base points and Enriques' unloading procedure are used to construct filtrations by complete ideals of C{x, y}. It follows a procedure for getting generators of the integral closure of an ideal.

Topological computation of local cohomology multiplicities.

We express the Lyubeznik numbers of the local ring of a complex isolated singularity in terms of Betti numbers of the associated real link.

Marqueurs de la filtration glomérulaire en pédiatrie [Glomerular filtration markers in pediatrics]

The assessment of glomerular filtration rate (GFR) is critical for the diagnosis and management of renal diseases in pediatric nephrology. Ideally, it requires the measurement of the renal clearance of a filtration marker. Inulin, an exogenous marker, is the only compound the excretion of which occurs exclusively by glomerular filtration, with no tubular handling. Therefore, inulin clearance provides the most accurate method to measure GFR and is considered as the "gold standard", at all ages including very premature neonates. However, inulin dearance is cumbersome and alternative methods are used in clinical practice. If urine is available, endogenous creatinine clearance is the most reliable method. When urine collection is difficult to obtain, GFR can be estimated by the plasma concentration of endogenous markers mainly eliminated by glomerular filtration, such as creatinine, or the more recently described cystatin C and beta 2-microglobulin. When the endogenous production of these markers is constant, their plasma concentration reflects glomerular filtration; it increases with decreasing renal function. However, in pediatric patients creatinine production depends on muscle mass, which significantly increases with linear growth, as well as age and gender. Mathematical formulas taking these parameters into account have thus been developed. Among these, the so-called "Schwartz formula" is often used and is a reliable estimate of GFR in children. Finally, radionuclide renal scans can be used to evaluate the separate glomerular function of each kidney.