Description:

Title: Algebraic vector bundles of rank 2 over smooth affine fourfolds

Abstract: To what extent do Chow-valued Chern classes determine the isomorphism class of an algebraic vector bundle? In this talk, I'll discuss some progress on this question for algebraic vector bundles of rank 2 over smooth affine fourfolds. These results imply some concrete cohomological classification results (e.g., over the complex numbers, there are exactly 9 isomorphism classes of rank 2 vector bundles over the complement of a smooth degree 3 hypersurface in P^4). I'll also highlight some possible computations that, if completed, would shed further light on this problem. This is joint work with Thomas Brazelton and Tariq Syed.