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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


636 SEO


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.

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Wenliang Zhang

Date posted

Feb 1, 2023

Date updated

Feb 1, 2023


Mahrud Sayrafi | (University of Minnesota)