Abstract
Let S be a projective smooth irreducible surface over ℂ. The subject of this paper is the study of coherent sheaves on multiple curves embedded in S. Coherent sheaves on singular nonreduced curves and their moduli spaces have been studied (cf. [2], [3]) and some general results have been obtained in [11] by M.-A. Inaba on moduli spaces of stable sheaves on reduced varieties of any dimension. In the case of curves we may hope of course much more detailed results.
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