Back to Algebraic Geometry Seminar: Fall 2011
Algebraic Geometry Seminar
Date: Tuesday, Nov 29, 2011
Time: 3:30PM - 4:30PM
Location: LCB 222
Wenbo Niu
Purdue University
Title |
A regularity bound for normal surfaces |
Abstract |
Castelnuovo-Mumford regulairy of varieties has drawn considerable attention in recent twenty years. There are two main general results about smooth curves and surfaces. Gruson-Peskine-Lazarsfeld showed that for a smooth curve X, one has (reg X \leq deg X - codim X+1). And Lazarsfeld showed that for a smooth surface the above result is still true. This regularity bound was formulated and conjectured by Eisenbud-Goto for any variety. In this talk we use duality theory to first give a quick proof for smooth curves and surfaces and then prove this bound for normal surfaces which have rational, Gorenstein elliptic or log canonical singularities. This is joint work with Lawrence Ein. |
Algebraic Geometry