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.
The linkage class of a grade three complete intersection
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abstract
Working over a field of characteristic zero, we give structure theorems for all grade three licci ideals and their minimal free resolutions. In particular, we completely classify such ideals up to deformation. The descriptions of their resolutions extend earlier results by Buchsbaum-Eisenbud, Brown, and Sanchez. Our primary tool is the theory of higher structure maps originating from the study of generic free resolutions of length three.
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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.