Joint seminar with COW

1.30pm David Eisenbud (MSRI and Berkeley): Fibers of a Generic Projection and Assymptotic Regularity

Abstract
Varieties were originally studied by comparing them with the hypersurfaces that are their generic projections—curves in the place and surfaces in three-space, for example. In low dimensions, the fibers of these generic projections are pretty well understood, but there are serious obstructions to extending this understanding to all dimensions. I’ll survey what’s known, explain some examples, and present a new conjecture about these fibers. A connection with the regularity of powers of an ideal (assymptotic regularity) plays an interesting role.

3pm Greg Sankaran (Bath): Locally symmetric varieties of orthogonal type

Abstract
For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than 19. I’ll describe some new(ish) results in this direction, making use of estimates for the space of modular forms for certain orthogonl groups. In particular the modular variety defined by the orthogonal group of the even unimodular lattice of signature (2, 8m+2) is of general type if m is at least 5.