Date: Wednesday, April 6 2022.
Time: 3:30 PM.
Venue: Seminar Hall.
Title: Asymptotic behaviour of certain length functions
Chennai Mathematical Institute.
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.