Faisceaux cohérents sur les courbes multiples

Abstract

Multiple primitive curves have been defined and studied by A. Banica and O. Forster. We introduce new invariants for coherent sheaves on these curves and define quasi locally free sheaves, which play the same role as locally free sheaves on smooth varieties. A more detailed study of torsion free sheaves is given for primitive curves of multiplicity 2.

45 pages - Added two sections removed prop. 8.2.1 (incorrect proof) added a supplementary necessary hypothesis in 3.1.5, 3.2, 3.3

References in corpus (4)

• Degeneration of moduli spaces and generalized theta functions
• Degeneration of SL(n)-bundles on a reducible curve
• Cohen-Macaulay Nilpotent Schemes
• Multiple Structures

Cited by in corpus (6)

• Reducible deformations and smoothing of primitive multiple curves
• On the irreducible components of the compactified Jacobian of a ribbon
• On the fixed locus of framed instanton sheaves on ${\mathbb{P}}^3$
• Sur les conditions d'existence des faisceaux semi-stables sur les courbes multiples primitives
• Moduli of sheaves supported on curves of genus two in a quadric surface
• Faisceaux sans torsion et faisceaux quasi localement libres sur les courbes multiples primitives