Tautological bundles on the Hilbert scheme of points

Brooke Ullery

To each line bundle L on a smooth variety X, we can associate a vector bundle E_L on the Hilbert scheme of n points on that variety. This vector bundle is tautological in the sense that its fiber over a general point is the sum of the fibers of L over the points in the corresponding subscheme of X. As these vector bundles arise so naturally, they come up in many settings such as embeddings of the Hilbert scheme in Grassmannians and syzygies of line bundles on curves. We will carefully compute the cohomology of E_L and its determinant, and then discuss a few applications of these computations

http://scgp.stonybrook.edu/video_portal/video.php?id=968

Simons- Workshop: Graduate Workshop on Geometry of Hilbert schemes