Generalized Newton Complementary Duals of Monomial Ideals
Katie Ansaldi, Kuei-Nuan Lin, Yi-Huang Shen
TL;DR
This paper introduces the concept of generalized Newton complementary duals for monomial ideals, exploring their algebraic properties and providing explicit cellular free resolutions, especially for degree two generated ideals.
Contribution
It defines generalized Newton complementary duals for monomial ideals and studies their properties, including free resolutions and fiber ring isomorphisms, with explicit constructions for degree two cases.
Findings
Duals have linear quotients and fiber ring isomorphisms
Cellular free resolutions constructed for duals of strongly stable ideals
Explicit resolution descriptions for degree two generated ideals
Abstract
Given a monomial ideal in a polynomial ring over a field, we define the generalized Newton complementary dual of the given ideal. We show good properties of such duals including linear quotients and isomorphisms between the special fiber rings. We construct the cellular free resolutions of duals of strongly stable ideals generated in the same degree. When the base ideal is generated in degree two, we provide an explicit description of cellular free resolution of the dual of a compatible generalized stable ideal.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory