Polarizations of powers of graded maximal ideals

Authors

• Ayah Almousa, University of KentuckyFollow
• Gunnar Fløystad, University of BergenFollow
• Henning Lohne, University of BergenFollow

Abstract

We give a complete combinatorial characterization of all possible polarizations of powers of the graded maximal ideal (x₁,x₂,…,x_m)ⁿ of a polynomial ring in m variables. We also give a combinatorial description of the Alexander duals of such polarizations. In the three variable case m=3 and also in the power two case n=2 the descriptions are easily visualized and we show that every polarization defines a (shellable) simplicial ball. We give conjectures relating to topological properties and to algebraic geometry, in particular that any polarization of an Artinian monomial ideal defines a simplicial ball.

Document Type

Article

Publication Date

5-1-2022

Notes/Citation Information

Publisher Copyright: © 2021 Elsevier B.V.

Digital Object Identifier (DOI)

10.1016/j.jpaa.2021.106924

Archival?

Archival

Repository Citation

Almousa, Ayah; Fløystad, Gunnar; and Lohne, Henning, "Polarizations of powers of graded maximal ideals" (2022). Mathematics Faculty Publications. 75.
https://uknowledge.uky.edu/math_facpub/75