Abstract
AbstractThis 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 and n is its multiplicity, then there is a filtration C1 = C ⊂ C2 ⊂ … ⊂ Cn = Y such that C is the reduced curve associated to Y, and for every P ∈ C, if z ∈ OY,P is an equation of C then (zi) is the ideal of Ci in OY,P. 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 OCi.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 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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