Differential Geometry Working Seminar

Paul Cusson, University of Waterloo

Holomorphic vector bundles over an elliptic curve

We'll go over the classification of holomorphic vector bundles over an elliptic curve, with a focus on the rank 1 and 2 cases. For the case of line bundles, we'll show that the space of degree 0 line bundles is isomorphic to the elliptic curve itself. The classification of rank 2 bundles rests on the existence of two special indecomposable 2-bundles of degree 0 and 1, which we will describe in detail. The general case for higher ranks would then follow essentially inductively

MC 5479