Polarizations of Powers of Maximal Ideals in a Polynomial Ring

Abstract:

We give a complete combinatorial characterization of all possible polarizations of powers of the maximal ideal $(x_1,x_2,\dotsc,x_n)$ in a polynomial ring of $n$ variables. We also give a combinatorial description of the Alexander duals of such polarizations. In the three variable case we show that every polarization defines a (shellable) simplicial ball. We conjecture that any polarization of an artinian monomial ideal defines a simplicial ball. This is joint work with Gunnar Fløystad.