Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view.

Teixidor i Bigas, Montserrat. "Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view.." Collectanea Mathematica 49.2-3 (1998): 527-548. <http://eudml.org/doc/41439>.

@article{TeixidoriBigas1998,
abstract = {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.},
author = {Teixidor i Bigas, Montserrat},
journal = {Collectanea Mathematica},
keywords = {Espacio de Moduli; Curvas algebraicas; Compacidad; Conjuntos estables; Fibrados; Polarización; Espacios vectoriales; compactifications of moduli spaces; family of curves; semistable bundles; curves in Grassmannians; nodal curve},
language = {eng},
number = {2-3},
pages = {527-548},
title = {Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view.},
url = {http://eudml.org/doc/41439},
volume = {49},
year = {1998},
}

TY - JOUR
AU - Teixidor i Bigas, Montserrat
TI - Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view.
JO - Collectanea Mathematica
PY - 1998
VL - 49
IS - 2-3
SP - 527
EP - 548
AB - 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.
LA - eng
KW - Espacio de Moduli; Curvas algebraicas; Compacidad; Conjuntos estables; Fibrados; Polarización; Espacios vectoriales; compactifications of moduli spaces; family of curves; semistable bundles; curves in Grassmannians; nodal curve
UR - http://eudml.org/doc/41439
ER -