LCM Duals of Monomial Ideals
Katie Ansaldi, Kuei-Nuan Lin
TL;DR
This paper introduces the concept of LCM-duals for monomial ideals, explores their algebraic properties, and provides explicit descriptions of their minimal free resolutions, revealing structural insights.
Contribution
It defines LCM-duals of monomial ideals and establishes their key properties, including isomorphisms and Cohen-Macaulayness, with explicit resolutions for strongly stable ideals.
Findings
LCM-duals are isomorphic to the special fiber of the original ideal.
LCM-duals of strongly stable ideals are normal Cohen-Macaulay Koszul domains.
Explicit minimal free resolutions are provided for these LCM-duals.
Abstract
Given a monomial ideal in a polynomial ring over a field, we define the LCM-dual of the given ideal. We show good properties of LCM-duals. Including the isomorphism between the special fiber of LCM-dual and the special fiber of given monomial ideal. We show the special fibers of LCM-duals of strongly stable ideals are normal Cohen-Macaulay Koszul domains. We provide an explicit describing of minimal free resolutions of LCM-duals of strongly stable ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory