On the Cohen-macaulayness of Certain Hyperplane Arrangements
نویسنده
چکیده
Inspired by the representation theory of rational Cherednik algebras, we consider whether certain rings corresponding to hyperplane arrangements in C satisfy the Cohen-Macaulay property. Specifically, for a partition λ = (λ1, . . . , λr) ` n we define a certain variety Xλ ⊂ C and study its coordinate ring C[Xλ]. The question which we work towards is: for which λ is Xλ CohenMacaulay? We consider the sub-question of when the coordinate ring of Xλ/Sn, defined below, is Cohen-Macaulay, and compute related information such as its Hilbert series and formulas for generating higher degree polynomials in terms of lower-degree gener-
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تاریخ انتشار 2014