Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)
Srikanth Iyengar (University of Utah)
Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg
Date: Tuesday, October 30
3:45 Srikanth Iyengar: Torsion in tensor powers of modules
The starting point of this talk is the observation that if a finitely generated module M over a noetherian (commutative!) domain R is NOT free, then its d-fold tensor-product has torsion for each d > rank_RM. In fact, when R is a regular local ring, torsion shows up already when d >= dim R; this is one of the central results in Auslander\\'s 1961 paper "Modules over unramified regular local rings". Recently Celikbas, Piepmeyer, R. Wiegand and I extended this result to certain modules over isolated hypersurface singularities; the preprint will be posted on the arXiv soon. My goal is to discuss some ideas that go into its proof. The main new tool is Hochster\\'s theta-function, and is inspired by recent work of Dao.
5:00 Vu Thanh: Linear resolutions of powers of edge ideals of anti-cycles.
Let $I$ be the edge ideal of an anticycle of length at least $5$. We will show that all powers $I^k$, for $k \ge 2$ have linear resolution.