Depth of an initial ideal

DOI10.1007/978-3-030-52111-0_6zbMATH Open1453.13081arXiv1907.12710OpenAlexW3148320332MaRDI QIDQ2221623

Akiyoshi Tsuchiya, Takayuki Hibi

Publication date: 2 February 2021

Abstract: Given an arbitrary integer $d>0$, we construct a homogeneous ideal $I$ of the polynomial ring $S=K[x_1,ldots,x_{3d}]$ in $3d$ variables over a filed $K$ for which $S/I$ is a Cohen--Macaulay ring of dimension $d$ with the property that, for each of the integers $0leqrleqd$, there exists a monomial order ${<}_r$ on $S$ with $mdepth(S/{min}_{{<}_r}(I))=r$, where ${min}_{{<}_r}(I)$ is the initial ideal of $I$ with respect to ${<}_r$.

Full work available at URL: https://arxiv.org/abs/1907.12710

zbMATH Keywords

Gröbner basisdepthinitial ideal

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

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