منابع مشابه
Combinatorial Shifting and Graded Betti Numbers
Let ∆ be a simplicial complex and I∆ its Stanley–Reisner ideal. It has been conjectured that, for each i and j, the graded Betti number βii+j(I∆) of I∆ is smaller than or equal to that of I∆c , where ∆ c is a combinatorial shifted complex of ∆. In the present paper the conjecture will be proved affirmatively. In particular the inequalities βii+j(I∆) ≤ βii+j(I∆lex) hold for all i and j, where ∆ ...
متن کاملShifting Operations and Graded Betti Numbers
The behaviour of graded Betti numbers under exterior and symmetric algebraic shifting is studied. It is shown that the extremal Betti numbers are stable under these operations. Moreover, the possible sequences of super extremal Betti numbers for a graded ideal with given Hilbert function are characterized. Finally it is shown that over a field of characteristic 0, the graded Betti numbers of a ...
متن کاملAlgebraic Shifting and Graded Betti Numbers
Let S = K[x1, . . . , xn] denote the polynomial ring in n variables over a field K with each deg xi = 1. Let ∆ be a simplicial complex on [n] = {1, . . . , n} and I∆ ⊂ S its Stanley–Reisner ideal. We write ∆e for the exterior algebraic shifted complex of ∆ and ∆c for a combinatorial shifted complex of ∆. Let βii+j(I∆) = dimK Tori(K, I∆)i+j denote the graded Betti numbers of I∆. In the present p...
متن کاملTight Combinatorial Manifolds and Graded Betti Numbers
In this paper, we study the conjecture of Kühnel and Lutz, who state that a combinatorial triangulation of the product of two spheres S×S with j ≥ i is tight if and only if it has exactly i+2j+4 vertices. To approach this conjecture, we use graded Betti numbers of Stanley–Reisner rings. By using recent results on graded Betti numbers, we prove that the only if part of the conjecture holds when ...
متن کاملMinimal Graded Betti Numbers and Stable Ideals
Let k be a field, and let R = k[x1, x2, x3]. Given a Hilbert function H for a cyclic module over R, we give an algorithm to produce a stable ideal I such that R/I has Hilbert function H and uniquely minimal graded Betti numbers among all R/J with the same Hilbert function, where J is another stable ideal in R. We also show that such an algorithm is impossible in more variables and disprove a re...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8878