An application of coherent systems to a Brill-Noether problem

Steven B. Bradlow, Oscar García-Prada

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)123-143
Number of pages21
JournalJournal fur die Reine und Angewandte Mathematik
Issue number551
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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