Factorialite de l΄algebre affine de certaines formes quadratiques
Factorisation de certains morphismes birationnels
Faisceaux pervers, transformation de Mellin et déterminants
Families of -symplectic metrics on full flag manifolds.
Families of -divisible groups with constant Newton polygon.
Families of reduced zero-dimensional schemes.
A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element...
Fano manifolds of degree ten and EPW sextics
O’Grady showed that certain special sextics in called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.
Fano Schemes of Linear Spaces on Hypersurfaces.
Fibré déterminant et courbes relatives
Fibrés de rang deux sur une courbe, fibré déterminant et fonctions thêta. II
Fibrés quadratiques et composantes connexes réelles.
Fibres vectoriels homogenes sur les varietes abeliennes qui sont des tores analytiques (rigides).
Filtrations of -modules
Finite orbit decomposition of real flag manifolds
Let be a connected real semi-simple Lie group and a closed connected subgroup. Let be a minimal parabolic subgroup of . It is shown that has an open orbit on the flag manifold if and only if it has finitely many orbits on . This confirms a conjecture by T. Matsuki.
Finiteness of cominuscule quantum -theory
The product of two Schubert classes in the quantum -theory ring of a homogeneous space is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on . We show that if is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to that take the marked points to general Schubert varieties and whose domains...
Finiteness of local fundamental groups for quotients of affine varieties under reductive groups.
Finiteness results for Abelian tree models
Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant§ refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We prove that if that symmetry group is Abelian, then the Zariski closures of these models are defined by polynomial equations of bounded degree, independent of the tree. Moreover, we show that there exists a polynomial-time membership test for that Zariski closure....
Fixed points for reductive group actions on acyclic varieties
Let be a smooth, affine complex variety, which, considered as a complex manifold, has the singular -cohomology of a point. Suppose that is a complex algebraic group acting algebraically on . Our main results are the following: if is semi-simple, then the generic fiber of the quotient map contains a dense orbit. If is connected and reductive, then the action has fixed points if .
Flag Manifolds and the Hook Formula.
Flag manifolds and the Landweber-Novikov algebra.