24/06/2010, 11:00 — 12:30 — Sala P3.10, Pavilhão de Matemática
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.