An ADE correspondence for grade three perfect ideals

Lorenzo Guerrieri; Xianglong Ni; Jerzy Weyman

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arXiv · 2407.02380

An ADE correspondence for grade three perfect ideals

Lorenzo Guerrieri·Xianglong Ni·Jerzy Weyman

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Abstract

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.

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Lorenzo Guerrieri, Xianglong Ni, Jerzy Weyman. 2024-07-02. An ADE correspondence for grade three perfect ideals. https://arxiv.org/abs/2407.02380

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