Projective Stability of Ruled Surfaces.
Projective surfaces with bi-elliptic hyperplane sections.
Projectivité des schémas en courbes sur un anneau de valuation discrète
Proof of Nadel’s conjecture and direct image for relative -theory
A “relative” -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
Proper intersection multiplicity and regular separation of analytic sets
We consider complex analytic sets with proper intersection. We find their regular separation exponent using basic notions of intersection multiplicity theory.
Properties of -p . p for Gorenstein surface singularities.
Propriétés du groupe tannakien des structures de Hodge -adiques et torseur entre cohomologies cristalline et étale
On donne des propriétés de la catégorie tannakienne des modules de Dieudonné filtrés sur un corps -adique (ces modules de Dieudonné jouent en -adique un rôle analogue aux structures de Hodge complexes). On prouve l’existence d’un foncteur fibre sur et la simple connexité du groupe associé. Ceci permet de montrer, sous la conjecture de Fontaine : “faiblement admissible entraîne admissible”, une conjecture de Rapoport et Zink décrivant le torseur entre cohomologie cristalline et étale, et de prouver...
Puissances extérieures, déterminants et cycles de Schubert
Pulling back cohomology classes and dynamical degrees of monomial maps
We study the pullback maps on cohomology groups for equivariant rational maps (i.e., monomial maps) on toric varieties. Our method is based on the intersection theory on toric varieties. We use the method to determine the dynamical degrees of monomial maps and compute the degrees of the Cremona involution.
Punctual Hilbert schemes and resolutions of multiple point singularities.