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An ADE correspondence for grade three perfect ideals
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Using the theory of "higher structure maps" from generic rings for free resolutions of length three, we give a classification of grade 3 perfect ideals with small type and deviation in local rings of equicharacteristic zero, extending the Buchsbaum-Eisenbud structure theorem on Gorenstein ideals and realizing it as the type D case of an ADE correspondence. We also deduce restrictions on Betti tables in the graded setting for such ideals.
Forward citations
Cited by 2 Pith papers
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Restrictions on the Betti tables of licci ideals
For several large classes of licci ideals, the number of generators is bounded by the largest shift in the last step of the graded free resolution, confirming part of three new conjectures.
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Generic models of licci ideals parametrized by Schur functors
Herzog classes of codimension-3 licci ideals are parametrized by pairs of partitions via a graph of direct links, with applications to Tor algebra structures.
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