Generic Generalized Diagonal Matrices
Commutative Algebra
2022-06-06 v3
Abstract
Generalized diagonal matrices are matrices that have two ladders of entries that are zero in the upper right and bottom left corners. The minors of generic generalized diagonal matrices have square-free initial ideals. We give a description of the facets of their Stanley-Reisner complex. With this description, we characterize the configuration of ladders that yield Cohen-Macaulay ideals. In the special case where both ladders are triangles, we show that the corresponding complex is vertex decomposable. Also in this case, we compute the height and multiplicity of the ideals.
Cite
@article{arxiv.2110.02264,
title = {Generic Generalized Diagonal Matrices},
author = {Vinh Nguyen and Hunter Simper},
journal= {arXiv preprint arXiv:2110.02264},
year = {2022}
}
Comments
18 pages, typos fixed from previous version and acknowledgements updated