Mono: an algebraic study of torus closures
Justin Chen
TL;DR
This paper investigates the algebraic properties of the mono operation, which extracts the largest monomial subideal from a given ideal, and compares Betti tables to understand their differences.
Contribution
It introduces and studies the mono operation in polynomial ideals, providing new insights into its algebraic behavior and effects on Betti tables.
Findings
mono(I) is the largest monomial subideal of I
Betti tables of I and mono(I) can differ significantly
Numerous examples illustrate the phenomena
Abstract
Given an ideal I in a polynomial ring, we consider the largest monomial subideal contained in I, denoted mono(I). We study mono as an interesting operation in its own right, guided by questions that arise from comparing the Betti tables of I and mono(I). Many examples are given throughout to illustrate the phenomena that can occur.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models