منابع مشابه
1 N ov 2 00 6 COMBINATORIAL SYMBOLIC POWERS
Symbolic powers of ideals are studied in the combinatorial context of monomial ideals. When the ideals are generated by quadratic squarefree monomials, the generators of the symbolic powers are obstructions to vertex covering in the associated graph and its blow-ups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of seca...
متن کاملComparing Powers and Symbolic Powers of Ideals
We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby ...
متن کاملm at h . A C ] 2 2 A ug 2 00 6 COMBINATORIAL SYMBOLIC POWERS SETH
Symbolic powers of ideals are studied in the combinatorial context of monomial ideals. When the ideals are generated by quadratic squarefree monomials, the generators of the symbolic powers are obstructions to vertex covering in the associated graph and its blow-ups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of seca...
متن کاملCombinatorial Congruences modulo Prime Powers
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f(x) ∈ Z[x]. We establish the congruence p f ∑ k≡r (mod pα) (n k ) (−1)f ( k − r pα ) ≡ 0 ( mod p ∑∞ i=α n/p i ) (motivated by a conjecture arising from algebraic topology) and obtain the following vast generalization of Lucas’ theorem: If α is greater than one, and l, s, t are nonnegative integers with s, t < p, then 1 ...
متن کاملLefschetz Principle Applied to Symbolic Powers
In this paper, an alternative proof is presented of the following result on symbolic powers due to Ein, Lazarsfeld and Smith (for the affine case over C) and to Hochster and Huneke (for the general case). Let A be a regular ring containing a field K. Let a be a radical ideal of A and let h be the maximum of the heights of its minimal primes. Then for all n, we have an inclusion a(hn) ⊂ an, wher...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.09.024