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.
ASJC Scopus subject areas
- Applied Mathematics