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The containment problem for ordinary and symbolic powers

Banff International Research Station for Mathematical Innovation and Discovery

This talk will be in part historical, and in part recent progress, on the containment problem for the ordinary and symbolic powers of self-radical ideals. If I is a self-radical ideal, the problem asks which symbolic power of I is contained in which ordinary power of I. We will in particular discuss two problems: the uniformity problem in complete local domains, and Harbourne’s conjecture for graded ideals in polynomial rings. In particular, the talk will present the recent work of Eloisa Grifo and myself proving Harbourne’s conjecture in the case the quotient ring is F-pure or dense F-pure type.

Mathematics; Commutative rings and algebras; Algebraic geometry; Algebraic structures

video/mp4

Author affiliation: University of Virginia

2017-11-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63592

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/