منابع مشابه
A pr 2 00 9 Consecutive cancellations in Betti numbers of local rings ∗
Let I be a homogeneous ideal in a polynomial ring P over a field. By Macaulay’s Theorem, there exists a lexicographic ideal L = Lex(I) with the same Hilbert function as I. Peeva has proved that the Betti numbers of P/I can be obtained from the graded Betti numbers of P/L by a suitable sequence of consecutive cancellations. We extend this result to any ideal I in a regular local ring (R,n) by pa...
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Let G be a simple graph on n vertices. LetH be either the complete graph Km or the complete bipartite graph Kr,s on a subset of the vertices in G. We show that G contains H as a subgraph if and only if βi,α(H) ≤ βi,α(G) for all i ≥ 0 and α ∈ Z. In fact, it suffices to consider only the first syzygy module. In particular, we prove that β1,α(H) ≤ β1,α(G) for all α ∈ Z if and only if G contains a ...
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A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory. The middle-perversity intersection homology with integral coefficients of a compact complex n-dimensional algebraic variety X with isolated singularities is well known to be...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07517-3