A level initial ideal of the 2-minors determinantal ideal
Francesco Bisio

TL;DR
This paper constructs a specific monomial order for the 2-minors determinantal ideal such that its initial ideal is level, Cohen-Macaulay, and exhibits favorable algebraic and combinatorial properties, including shellability.
Contribution
It introduces a monomial order making the initial ideal of the 2-minors determinantal ideal level and Cohen-Macaulay, and compares Betti tables and shellability properties.
Findings
Initial ideal is level and Cohen-Macaulay.
Betti tables of the ideal and initial ideal are compared.
Shellability of associated simplicial complex is proven for m<n.
Abstract
For a field, let a matrix of variables and We consider the determinantal ideal generated by the -minors of In this paper we find a suitable monomial order over such that , the initial ideal of with respect to that order, is level, namely, it is Cohen-Macaulay and the socle of an Artinian reduction of the -graded algebra is concentrated in only one degree. Moreover, we compare the Betti tables of with the tables of its initial ideals. In the last section, we prove the shellability of the simplicial complex naturally associated to in the case
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Advanced Combinatorial Mathematics
