Polarizations of powers of graded maximal ideals
Journal article, Peer reviewed
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Original versionJournal of Pure and Applied Algebra. 2022, 226 (5), 106924. 10.1016/j.jpaa.2021.106924
We give a complete combinatorial characterization of all possible polarizations of powers of the graded maximal ideal (x1, x2, . . . , xm) 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.