منابع مشابه
THE LCM-LATTICE in MONOMIAL RESOLUTIONS
Describing the properties of the minimal free resolution of a monomial ideal I is a difficult problem posed in the early 1960’s. The main directions of progress on this problem were: • constructing the minimal free resolutions of special monomial ideals, cf. [AHH, BPS] • constructing non-minimal free resolutions; for example, Taylor’s resolution (cf. [Ei, p. 439]) and the cellular resolutions •...
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Let M be a monomial ideal in the polynomial ring S = k[x1, . . . , xn] over a field k. We are interested in the problem, first posed by Kaplansky in the early 1960’s, of finding a minimal free resolution of S/M over S. The difficulty of this problem is reflected in the fact that the homology of arbitrary simplicial complexes can be encoded (via the Stanley-Reisner correspondence [BH,Ho,St]) int...
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We characterize the lcm lattices that support a monomial ideal with a pure resolution. Given such a lattice, we provide a construction that yields a monomial ideal with that lcm lattice and whose minimal free resolution is pure.
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Let P be a finite partially ordered set with unique minimal element 0̂. We study the Betti poset of P , created by deleting elements q ∈ P for which the open interval (0̂, q) is acyclic. Using basic simplicial topology, we demonstrate an isomorphism in homology between open intervals of the form (0̂, p) ⊂ P and corresponding open intervals in the Betti poset. Our motivating application is that the...
متن کاملCellular Resolutions of Monomial Modules
We construct a canonical free resolution for arbitrary monomial modules and lattice ideals. This includes monomial ideals and defining ideals of toric varieties, and it generalizes our joint results with Irena Peeva for generic ideals [BPS],[PS]. Introduction Given a field k, we consider the Laurent polynomial ring T = k[x 1 , . . . , x ±1 n ] as a module over the polynomial ring S = k[x1, . . ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1999
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1999.v6.n5.a5