Division algebras and moduli spaces

Aidan Schofield

Abstract: By taking account of certain Brauer classes naturally associated to orbit problems, we can settle a number of outstanding rationality problems on moduli spaces. Thus we can show that the moduli space of vector bundles of rank r and determinant line bundle D is a rational variety when the highest common factor of r and d, the degree of D, is 1. For moduli spaces of vector bundles on the projective plane we are able to show that these are always birational to the centre of a suitable generic division algebra and the same is true for moduli spaces of representations of quivers.

created Fri Mar 17 17:33:12 PST 2000