The Alexander Duality Functors and Local Duality with Monomial Support

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Computational Algebraic Geometry (2003, background): “Recently Eagon and Reiner [27] showed that the betti numbers appear on a single row (of the Macaulay 2 betti diagram) iff the Alexander dual of ∆ is arithmetically Cohen-Macaulay (the Cohen-Macaulay property is discussed in Chapter 10, see Miller [68] for Alexander duality).”
Multigraded Castelnuovo-Mumford Regularity (2003, background): “2 in [28], we deduce that H i B(M) = H (Č ⊗S M) for all S-modules M .”
Planar graphs as minimal resolutions of trivariate monomial ideals (2002, methodology): “Considering the Theorem 8.4, the duality result here essentially falls under the umbrella of duality for resolutions of monomial ideals [ Mil00a , Section 4.2].”
Gröbner geometry of Schubert polynomials (2001, background): “r of ways to prove the existence of ﬁnite irreducible resolutions. One could apply the Alexander duality functor with respect to some degree a ∈Zm to a free resolution of the Alexander dual module Γa [Mil00a]. Alternatively, one can take the Nm-graded part of a Zm-graded injective resolution of Γ; t”