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

Collectanea Mathematica (1998)

- Volume: 49, Issue: 2-3, page 527-548
- ISSN: 0010-0757

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topTeixidor 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 -

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