Factorisation of generalised theta functions. I.
Factorization of rank two theta functions. II. Proof of the Verlinde formula.
Faisceaux cohérents sur les courbes multiples.
This paper is devoted to the study of coherent sheaves on non reduced curves that can be locally embedded in smooth surfaces. If Y is such a curve then there is a filtration C ⊂ C2 ⊂ ... ⊂ Cn = Y such that C is the reduced curve associated to Y, and for very P ∈ C there exists z ∈ OY,P such that (zi) is the ideal of Ci in OY,P. We define, using canonical filtrations, new invariants of coherent sheaves on Y: the generalized rank and degree, and use them to state a Riemann-Roch theorem for sheaves...
Fibrés Vectoriels Semi-Stables sur une Courbe de Genre Deux et Association des Points dans L’espace Projectif
2000 Mathematics Subject Classification: 14D20, 14J60.The aim of this paper is to prove that a certain involution on the moduli space of stable bundles on a curve of genus two, can be viewed as a geometric operation on the corresponding set of points in projective space.
Fibrés vectoriels spéciaux
Fourier-Mukai transforms and stable bundles on elliptic curves.
Fragmented deformations of primitive multiple curves
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...
Funtori integrali e fasci di Picard su varietà jacobiane e di Prym