Compactified Jacobians of curves with spine decompositions

Details Compactified Jacobians of curves with spine decompositions Compactified Jacobians of curves with spine decompositions

2007-12-07

arxiv.org/abs/0712.1176v1

Mathematics

Algebraic Geometry

Scientific paper

A curve, that is, a connected, reduced, projective scheme of dimension 1 over an algebraically closed field, admits two types of compactifications of its (generalized) Jacobian: the moduli schemes of P-quasistable torsion-free, rank-1 sheaves and Seshadri's moduli schemes of S-equivalence classes of semistable torsion-free, rank-1 sheaves. Both are constructed with respect to a choice of polarization. The former are fine moduli spaces which were shown to be complete; here we show that they are actually projective. The latter are just coarse moduli spaces. Here we give a sufficient condition for when these two types of moduli spaces are equal.

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