Description
Commutative algebra seminar
Thursday, 4 October, 2018
Room 215
2.00-3.30
Speaker: J. K. Verma
Title: The Hoskin-Deligne formula for complete ideals in two-dimensional regular local rings.
Abstract: Let I be a complete m-primary ideal in a two dimensional regular local ring R.
The Hoskin-Deligne (HD) formula expresses the length of the Artin local ring R/I in terms of
the m-adic order of the transforms of I in various local quadratic transforms of R.
It uses a structure theorem of Zariski and Abhyankar about two dimensional regular
local rings which birationally dominate R. The HD formula implies several fundamental
theorems about complete ideals proved by Zariski, Lipman, Rees and Huneke-Sally. We
shall prove these in a series of talks.