Math @ Duke

Publications [#243918] of Ezra Miller
Papers Published
 Miller, E, CohenMacaulay quotients of normal semioroup rings via irreducible resolutions,
Mathematical Research Letters, vol. 9 no. 1
(2002),
pp. 117128 [MR2003a:13015], [math.AC/0110096]
(last updated on 2017/12/17)
Abstract: For a radical monomial ideal I in a normal semigroup ring κ[Q], there is a unique minimal irreducible resolution 0 → κ[Q]/I → W̄0 → W̄1 ... by modules W̄i of the form ⊕jk[Fij], where the Fij are (not necessarily distinct) faces of Q. That is, W̄i is a direct sum of quotients of κ[Q] by prime ideals. This paper characterizes CohenMacaulay quotients κ[Q]/I as those whose rainimal irreducible resolutions are linear, meaning that W̄i is pure of dimension dim(κ[Q]/I)  i for i ≥ 0. The proof exploits a graded ringtheoretic analogue of the Zeeman spectral sequence [Zee63], thereby also providing a combinatorial topological version involving no commutative algebra. The characterization via linear irreducible resolutions reduces to the EagonReiner theorem [ER98] by Alexander duality when Q = Nd.


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