Year: 2026
Type: preprint
Abstract: Let $L\subseteq\mathbb Z^4$ be a rank-three lattice possessing an admissible basis, and let $S=K[x_1,\ldots,x_4]$ be the polynomial ring over a field $K$. We show that the associated lattice ideal $I_L \subset S$ is generic and that $S/I_L$ is a Cohen--Macaulay ring. We also identify the neighbors of the origin in $L$ and the indispensable binomials of $I_L$. Moreover, we prove that the Betti numbers of $S/I_L$ are $β_0(S/I_L)=1$, $β_1(S/I_L)=7$, $β_2(S/I_L)=12$, and $β_3(S/I_L)=6$. In addition, we show that $I_L$ is a set-theoretic complete intersection over an arbitrary field.
Source: arXiv (Cornell University)
Author: Katsabekis, Anargyros
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170034542