Back to Commutative Algebra Seminar: Spring 2022
Commutative Algebra Seminar
Date: Friday, Mar 18, 2022
Time: 2:00PM - 3:00PM
Location: LCB 222
Swaraj Pande
University of Michigan
Title |
Multiplicities of Jumping Numbers |
Abstract |
Multiplier ideals are refined invariants of singularities of algebraic varieties. They give rise to other numerical invariants, for example, the log canonical threshold and more generally, jumping numbers. This talk is about another related invariant, namely multiplicities of jumping numbers. For an m-primary ideal I in the local ring of a smooth complex variety, multiplicities of jumping numbers measure the difference between successive multiplier ideals of I. The main result is that these multiplicities naturally fit into a quasi-polynomial. We will also discuss when the various components of this quasi-polynomial have the highest possible degree, relating it to the Rees valuations of I. As a consequence, we derive some formulas for a subset of jumping numbers of m-primary ideals. Time permitting, we will consider the special case of monomial ideals where these invariants have a combinatorial description in terms of the Newton polyhedron. |
Commutative Algebra