Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Vector bundles on $P^1$ bundles
Seminar | September 10 | 5-6 p.m. | 939 Evans Hall
Hannah Larson, Stanford University
Every vector bundle on $P^1$ splits as a direct sum of line bundles. Given a vector bundle $E$ on a $P^1$ bundle $PW \to B$, the base $B$ is stratified by subvarieties defined by the condition that the restriction of $E$ to the fibers has a certain splitting type. It is natural to ask how to find the classes of the closures of these strata in the Chow ring of $B$. I will answer this question with an inductive algorithm. I will also discuss an application to the Brill-Noether theory of k-gonal curves.