Back to Commutative Algebra Seminar: Spring 2019
Commutative Algebra Seminar
Date: Friday, Feb 8, 2019
Time: 2:30PM - 3:20PM
Location: LCB 222
Patricia Klein
University of Kentucky
Title |
Lech's inequality and the Stückrad-Vogel conjecture |
Abstract |
Let (R, m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. Let e(I,M) denote the Hilbert-Samuel multiplicity of M on the ideal I. Lech’s inequality states that the set {length(R/I)/e(I,R)}, as I runs through all m-primary ideals, is bounded below by 1/d!e(m,R). Stückrad and Vogel showed that this set is not in general bounded above. However, they conjectured that whenever the completion of M is equidimensional that {length(M/IM)/e(I,M)} will indeed be bounded above. We prove this conjecture. This talk is based on joint work with Linquan Ma, Pham Hung Quy, Ilya Smirnov, and Yongwei Yao. |
Commutative Algebra