Multicomplex Configurations: a case study in Gorenstein Liaison
Commutative Algebra
2025-07-15 v1
Abstract
We introduce and investigate multicomplex configurations, a class of projective varieties constructed via specialization of the polarizations of Artinian monomial ideals. Building upon geometric polarization and geometric vertex decomposition, we establish conditions under which such configurations retain desirable algebraic properties. In particular, we show that, given suitable choices of linear forms for substitution, the resulting ideals admit Gr\"obner bases with prescribed initial ideals and are in the Gorenstein liaison class of a complete intersection.
Cite
@article{arxiv.2507.10357,
title = {Multicomplex Configurations: a case study in Gorenstein Liaison},
author = {Patricia Klein and Jenna Rajchgot and Alexandra Seceleanu},
journal= {arXiv preprint arXiv:2507.10357},
year = {2025}
}