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arXiv · 2507.10357

Multicomplex Configurations: a case study in Gorenstein Liaison

Patricia Klein·Jenna Rajchgot·Alexandra Seceleanu
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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.

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Patricia Klein, Jenna Rajchgot, Alexandra Seceleanu. 2025-07-14. Multicomplex Configurations: a case study in Gorenstein Liaison. https://arxiv.org/abs/2507.10357

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