Moduli spaces of vector bundles on families of non-singular curves are usually compactified by considering (slope)semistable bundles on stable curves. Alternatively, one could consider Hilbert-stable curves in Grassmannians. We study some properties of the latter and compare them with similar properties of curves coming from the former compactification. This leads to a new interpretation of the moduli space of (semi)stable torsion-free sheaves on a fixed nodal curve. One can present it as a quotient of a moduli space of torsion-free sheaves on a variable curve in such a way that each class has a locally-free representative.
@article{urn:eudml:doc:41439,
title = {Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view.},
journal = {Collectanea Mathematica},
volume = {49},
year = {1998},
pages = {527-548},
zbl = {0932.14015},
mrnumber = {MR1677092},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41439}
}
Teixidor i Bigas, Montserrat. Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view.. Collectanea Mathematica, Tome 49 (1998) pp. 527-548. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41439/