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Faisceaux sans torsion et faisceaux quasi localement libres sur les courbes multiples primitives
Author(s) -
Drézet Jean–Marc
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810781
Subject(s) - mathematics , pure mathematics , sheaf , irreducibility , torsion (gastropod) , coherent sheaf , medicine , surgery
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 and n is its multiplicity, then there is a filtration C 1 = C ⊂ C 2 ⊂ … ⊂ C n = Y such that C is the reduced curve associated to Y , and for every P ∈ C , if z ∈ O Y,P is an equation of C then ( z i ) is the ideal of C i in O Y,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 O 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 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)