Rees Algebras of Unit Interval Determinantal Facet Ideals
Ayah Almousa, Kuei-Nuan Lin, and Whitney Liske
TL;DR
This paper uses SAGBI basis techniques to analyze the algebraic properties of Rees algebras and special fiber rings of unit interval determinantal facet ideals, revealing their normality, Cohen-Macaulayness, and Koszul property.
Contribution
It provides explicit Gr"obner bases and proves that these ideals are of fiber type with Koszul, normal Cohen-Macaulay, and rational singularity properties.
Findings
Rees algebras and special fiber rings are normal Cohen-Macaulay domains.
They are of fiber type and have Koszul property.
The rings have rational singularities.
Abstract
Using SAGBI basis techniques, we find Gr\"obner bases for the presentation ideals of the Rees algebras and special fiber rings of unit interval determinantal facet ideals. In particular, we show that unit interval determinantal facet ideals are of fiber type and that their special fiber rings are Koszul. Moreover, their Rees algebras and special fiber rings are normal Cohen-Macaulay domains and have rational singularities.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models