Faisceaux sans torsion et faisceaux quasi localement libres sur les courbes multiples primitives

الأصل · EN

This paper is devoted to the study of some 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 by subschemes Cᵢ such that C₁ is the reduced curve associated to Y, and that for every P in C, if z is an equation of C₁ in the local ring of Y at P, then (zⁱ) is the ideal of Cᵢ. A coherent sheaf on Y is called torsion free if it does not have any non zero subsheaf with finite support. We prove that torsion free sheaves are reflexive. We study then the quasi locally free sheaves, i.e. sheaves which are locally isomorphic to direct sums of the structure sheaves of the Cᵢ. We define an invariant for these sheaves, the complete type, and prove the irreducibility of the set of sheaves of given complete type. We study the generic quasi locally free sheaves, with applications to the moduli spaces of stable sheaves on Y.