Commutative Algebra Seminar
Tuesday, 13 Feb, 3 pm—4 pm
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Venue: Room 215
Host: Tony J. Puthenpurakal
Speaker: Sudeshna Roy
Affiliation: TIFR Bombay
Title: Epsilon multiplicity in two-dimensional standard graded algebras
Abstract: The notion of epsilon multiplicity, a generalization of the Hilbert-Samuel multiplicity, was introduced by B. Ulrich and J. Validashti to detect the integral dependence of arbitrary ideals. This invariant is difficult to handle as there are examples where it can be irrational and the epsilon function is very far from being polynomial-like. Let $A$ be a standard graded normal domain of dimension two over a field with the unique homogeneous maximal ideal $m$. Let $I$ be a homogeneous ideal in $A$. Our objective is to show that the epsilon multiplicity of $I$ is a rational number.