Speaker: Winfried Bruns, University of Osnabrueck, Germany.
Date/Time: 17 September 2021, 5:30pm IST/ 12:00pm GMT / 8:00am EDT
(joining time 5:15pm IST).
Google meet link: meet.google.com/xso-hhub-vwr
Title: Castelnuovo-Mumford regularity over general base rings.
Abstract: Our talk has two goals. The first is to give a short
introduction to Castelnuovo-Mumford regularity for standard graded rings
over general base rings. The second is to present a simple and concise
proof of a classical result of Cutkosky, Herzog and Trung and,
independently, Kodiyalam asserting that the regularity of powers of a
homogeneous ideal is eventually a linear function of the exponent in this
generality. Finally we show how the flexibility of working over general
base rings can be used to give a simple proof for the characterization of
"linear powers" in terms of the Rees algebra.
This is joint work with Aldo Conca and Matteo Varbaro. See
"Castelnuovo-Mumford regularity and powers", arXiv:2107.14734. An
extensive version will be part of the forthcoming book "Determinants,
Gröber bases and cohomology" with Conca, Varbaro and Claudiu Raicu.
For more information and links to previous seminars, visit the website of
VCAS:
https://sites.google.com/view/virtual-comm-algebra-seminar