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Free resolutions constructed from bigradings on Lie algebras

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arxiv 2304.01381 v1 pith:OAESJEDY submitted 2023-04-03 math.AC math.AG

Xianglong Ni , Jerzy Weyman This is my paper · ORCID
classification math.ACmath.AG
keywords idealsfreeresolutionsalgebrasbettibigradingsbuchsbaumcell
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We construct two families of free resolutions that resolve the ideals of certain opposite Schubert varieties restricted to the big open cell. We conjecture that these examples have genericity properties translating to structure theorems for perfect ideals with given Betti numbers, extending the well-known theorem of Buchsbaum and Eisenbud on Gorenstein ideals of codimension three.

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  1. Generic models of licci ideals parametrized by Schur functors

    math.AC 2025-06 conditional novelty 6.0 of 10

    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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