Room P3.10, Mathematics Building

Peter Newstead, University of Liverpool

Coherent systems on algebraic curves: moduli spaces of vector bundles and of coherent systems; Brill-Noether loci; basic properties.

A coherent system on an algebraic curve (or Riemann surface) is a pair consisting of a vector bundle (algebraic or holomorphic) and a subspace of its space of sections. These are direct generalisations of the classical linear systems studied since the mid 19th century. Moduli spaces for coherent systems exist using a concept of stability dependent on a real parameter. The purpose of these lectures is to introduce coherent systems and describe the current state of knowledge.