TY - JOUR
T1 - An application of coherent systems to a Brill-Noether problem
AU - Bradlow, Steven B.
AU - García-Prada, Oscar
PY - 2002
Y1 - 2002
N2 - A coherent system (CS) consists of a holomorphic bundle together with a subspace of its space of holomorphic sections. There is a notion of stability for this type of 'augmented bundle', with resulting moduli spaces of stable objects. The definition of stability, and hence the moduli spaces, depend on a real parameter. At large values of the parameter, the moduli spaces are easy to describe. At small values of the parameter there is a natural map from the CS moduli spaces to Brill-Noether loci in the moduli spaces of semistable bundles. We use these observations to reinterpret results of Brambila-Paz, Grzegorczyk, and Newstead on the non-emptiness of Brill-Noether loci, and to suggest a method for obtaining more general results of the same sort.
AB - A coherent system (CS) consists of a holomorphic bundle together with a subspace of its space of holomorphic sections. There is a notion of stability for this type of 'augmented bundle', with resulting moduli spaces of stable objects. The definition of stability, and hence the moduli spaces, depend on a real parameter. At large values of the parameter, the moduli spaces are easy to describe. At small values of the parameter there is a natural map from the CS moduli spaces to Brill-Noether loci in the moduli spaces of semistable bundles. We use these observations to reinterpret results of Brambila-Paz, Grzegorczyk, and Newstead on the non-emptiness of Brill-Noether loci, and to suggest a method for obtaining more general results of the same sort.
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U2 - 10.1515/crll.2002.079
DO - 10.1515/crll.2002.079
M3 - Article
AN - SCOPUS:0041667935
SP - 123
EP - 143
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 551
ER -