Date : March 11, Friday
Time : 11:30-12:30
Link :
https://meet.google.com/bmi-aoav-tgi?authuser=0
Title: Asymptotic behaviour of certain length functions.
Abstract: The notion of epsilon multiplicity was originally defined by B.
Ulrich and J. Validashti as a limsup and they used it to detect integral
dependence of modules. It is important to know if the limsup can be
replaced by a limit. In this talk we shall see that the relative epsilon
multiplicity of reduced standard graded algebras over an excellent local
ring exists as a limit. However, the associated length function can be
quite complicated. We explore certain situations when the symbolic (multi)
Rees algebra is finitely generated. In such cases, the associated
(multigraded) length function exhibits polynomial-like behaviour.