Generalizing the Borel property
Christopher A. Francisco, Jeffrey Mermin, and Jay Schweig
TL;DR
This paper introduces Q-Borel ideals, a new class of monomial ideals closed under specific Borel moves from a poset, exploring their structure and properties to bridge Borel and arbitrary monomial ideals.
Contribution
It defines Q-Borel ideals and investigates their decompositions and homological properties, providing a framework that interpolates between Borel and general monomial ideals.
Findings
Q-Borel ideals generalize classical Borel ideals.
Decomposition methods for Q-Borel ideals are developed.
Homological properties of Q-Borel ideals are characterized.
Abstract
We introduce the notion of Q-Borel ideals: ideals which are closed under the Borel moves arising from a poset Q. We study decompositions and homological properties of these ideals, and offer evidence that they interpolate between Borel ideals and arbitrary monomial ideals.
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