Seminar Algebra and Geometry: Paolo Mantero (Purdue University)

Minimal representatives of even liaison classes

A vast part of literature on CI-linkage has addressed questions relative to the most relevant, and well-behaved, class of ideals in linkage: licci ideals. However, for a non-licci ideal I, there are few results describing the structure of the linkage class of I.

In this talk we introduce a theoretical definition for 'minimal' representatives in any even linkage class. We show that these ideals
exist under reasonable assumptions on the linkage class, and, in general, if they exist they are essentially unique.
We then show that these ideals minimize homological invariants (e.g. Betti numbers, multiplicity, etc.) and they enjoy the best homological and local properties among all the ideals in their even linkage class. This justifies why they are, in some sense, the `best' possible ideals in the even linkage class.

We provide several classes of ideals that are the minimal representatives of their even linkage classes (including determinantal ideals) and, if time permits, show an easy application to produce more evidence towards the Buchsbaum-Eisenbud-Horrocks Conjecture.

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