Structural decomposition of monomial resolutions
نویسندگان
چکیده
منابع مشابه
Monomial Resolutions
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 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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We study the structure of (minimal) free resolutions of monomial ideals over a polynomial ring. This has been a very active area of research, and a number of new ideas and approaches were introduced in the last decade. In this paper, we introduce three new notions: 1) We introduce the frame of a free resolution. The frame is a complex of vector spaces which encodes the structure of the resoluti...
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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 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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.09.003