Your browser is unsupported

We recommend using the latest version of IE11, Edge, Chrome, Firefox or Safari.

Jan 30 2023

Commutative Algebra Seminar: Bounding the Multigraded Regularity of Powers of Ideals, by Mahrud Sayrafi

January 30, 2023

3:00 PM - 3:50 PM

Location

636 SEO

Address

Chicago, IL

Mahrud Sayrafi (University of Minnesota): Bounding the Multigraded Regularity of Powers of Ideals

Building on a result of Swanson, Cutkosky--Herzog--Trung and Kodiyalam described the surprisingly predictable asymptotic behavior of Castelnuovo--Mumford regularity for powers of ideals on a projective space P^n: given an ideal I, there exist integers d and e such that for large enough n the regularity of I^n is exactly dn+e.
Through a medley of examples we will see why asking the same question about an ideal I in the total coordinate ring S of a smooth projective toric variety X is interesting. After that I will summarize the ideas and methods we used to bound the region reg(I^n) as a subset of Pic(X) by proving that it contains a translate of reg(S) and is contained in a translate of Nef(X), with each bound translating by a fixed vector as n increases. Along the way will see some surprising behavior for multigraded regularity of modules. This is joint work with Juliette Bruce and Lauren Cranton Heller.

Please click here to make changes to, or delete, this seminar announcement.

Contact

Wenliang Zhang

Date posted

Feb 1, 2023

Date updated

Feb 1, 2023

Speakers

Mahrud Sayrafi | (University of Minnesota)