Isomorphisms Between Local Cohomology Modules As Truncations of Taylor Series

Abstract

Let R be a standard graded polynomial ring that is finitely generated over a field, and let I be a homogenous prime ideal of R. Bhatt, Blickle, Lyubeznik, Singh, and Zhang examined the local cohomology of R/I t , as t grows arbitrarily large. Such rings are known as thickenings of R/I. We consider R = F[X] where F is a field of characteristic 0, X is a 2 × m matrix, and I is the ideal generated by size two minors. We give concrete constructions for the local cohomology modules of thickenings of R/I. Bizarrely, these local cohomology modules can be described using the Taylor series of natural log.