Commutative Algebra Seminar: Bounding the Multigraded Regularity of Powers of Ideals, by Mahrud Sayrafi
January 30, 2023
3:00 PM - 3:50 PM
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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.
Feb 1, 2023
Feb 1, 2023