Mathematics Colloquium
Date:Lincoln NE 68508
Affiliation: UNL
Local Host: Lucho Avramov
Title: Regularity of Projective Varieties via Projections.
Additional Public Info:
Let X be a projective variety embedded in a projective space PN .
The regularity of X is an important measure of how complicated the
geometry of X and the embedding are. For example, it bounds the de-
gree of the defining equations of X. The study of regularity dated back to Castelnuovo more than a hundred years ago and was revolutionalized by Mumford in the sixties. Motivated by the work of Gruson, Lazarsfeld and Peskine bounding the regularity of projecive curves, in the eighties, Eisenbud and Goto conjectured that the regularity can be bounded by the degree minus the codimension of X. Their idea was that the regularity of X is bounded by the regularity of some of its projection. In the talk, I will introduce the conjecture, its history and a new approach toward the conjecture. Lots of examples will be presented.
Refreshments will be served in 348 Avery, 3:30 - 4:00. The talk is free and open to the public.