Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Free Resolutions, Linkage, and Representation Theory - 5
In the final talk, we give a sketch of a conjectural ADE correspondence for perfect ideals and show how it unifies a long list of classical results. In particular, Hilbert-Burch and Buchsbaum-Eisenbud arise as type A and type D cases of this correspondence, explaining why grade 2 perfect ideals and grade 3 Gorenstein ideals are so special. We then prove the conjecture for grade 3 perfect ideals (assuming equicharacteristic zero). To pique your interest, here is one formulation of the main conjecture in terms of a bizarre inequality:
Conjecture. Suppose S is a local Noetherian ring, I is a perfect ideal of grade c > 1 in S generated by c+d elements, and Ext^c(S/I,S) is generated by t elements. If 1/(c-1) + 1/(d+1) + 1/(t+1) > 1, then I is in the linkage class of a complete intersection.