Contribution effective dans le réel
Le calcul de la forme hermitienne canonique pour un polynome homogène à singularité isolée.
A propos d'une conjecture de R. Hartshorne.
Un théorème d'algébraicité intermédiaire.
Dévelopment asymptotique des fonctions obtenues par intégration sur les fibres.
Forme hermitienne canonique sur la cohomologie de la fibre de Milnor d'une hypersurface à singularité isolée.
Contribution effective de la monodromie aux développements asymptotiques
Le reseau L2 d'un Systeme holonome regulier.
Fonctions holomorphes sur l'espace des cycles
Singular holomorphic functions for which all fibre-integrals are smooth
For a germ (X,0) of normal complex space of dimension n + 1 with an isolated singularity at 0 and a germ f: (X,0) → (ℂ,0) of holomorphic function with df(x) ≤ 0 for x ≤ 0, the fibre-integrals , are on ℂ* and have an asymptotic expansion at 0. Even when f is singular, it may happen that all these fibre-integrals are . We study such maps and build a family of examples where also fibre-integrals for , the Grothendieck sheaf, are .
Around the intersection form of an isolated singularity of hypersurface
La conjecture de R. Hartshorne pour les hypersurfaces lisses de Pn.
Asymptotique des intégrales-fibres
Asymptotics of eigensections on toric varieties
Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities for eigensections approaching a semiclassical ray. Here is a normal compact toric variety and is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch....
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