Algebra and Geometry Seminar

I'll begin with a discussion of the classification of vector bundles on P1 and explain what natural cohomology means in this context. Then I'll consider the case of vector bundles on P1 x P1. In general vector bundles on surfaces are more complicated but a useful tool allows one to reduce many problems about vector bundles to questions of linear algebra. This is the theory of monads. I'll discuss monads and show how they are used to prove a conjecture of Eisenbud and Schreyer about vector bundles on P1 x P1 with natural cohomology.