Vector Bundles, Locally Free Sheaves and Divisors on a Curve

In this post, I'll be summarizing the basics of the correspondence between vector bundles, locally free sheaves and divisors on a smooth curve (defined over an algebraically closed field $latex k$ of characteristic zero) together with some of their individual properties. Locally free sheaves and Vector bundles: Proposition 1: a) A coherent sheaf $latex \mathcal{E}$ on a … Continue reading Vector Bundles, Locally Free Sheaves and Divisors on a Curve

Classification of Vector Bundles on Elliptic curves

I'm supposed to give a talk on this subject for one of my courses, so I consider this post as a "pre-exposition." I learned from and heavily used the great exposition "Vector bundles on curves" by Montserrat Teixidor I Bigas in this post. I wrote up the pre-requisites here. In 1957, Atiyah in this famous paper "Vector bundles over … Continue reading Classification of Vector Bundles on Elliptic curves