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Moduli spaces of vector bundles on reducible curves. (English) Zbl 0836.14012

C. S. Seshadri [cf. “Fibrés vectoriels sur les courbes algébriques”, Astérisque 96 (1982; Zbl 0517.14008)] defined a moduli space of torsion-free sheaves on singular curves that are semi-stable for a given polarization. These moduli spaces turn out to be reducible when the curve itself is a nodal reducible curve. This paper gives a description of the components of the moduli space similar to the one given in rank one by T. Oda and C. S. Seshadri [Trans. Am. Math. Soc. 253, 1-90 (1979; Zbl 0418.14019)]. Each component of the moduli space corresponds to a different distribution of degrees among the components of the reducible curve. The intersection of components in the moduli space correspond to torsion-free non locally-free sheaves. The changes in the moduli space that occur with a change of polarization have recently been studied by the author [cf. “Moduli spaces of semistable sheaves on reducible curves and change of polarization” (preprint)].

MSC:

14H10 Families, moduli of curves (algebraic)
14H60 Vector bundles on curves and their moduli
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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