Summer Lectures in Geometry 

24/06/2010, 15:30 — 17:00 — Room P3.10, Mathematics Building
Peter Newstead, University of Liverpool

Coherent systems on algebraic curves: existence results for stable coherent systems

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.