On the Lyubeznik numbers of a local ring
نویسندگان
چکیده
منابع مشابه
On the Lyubeznik Numbers of a Local Ring
We collect some information about the invariants λp,i(A) of a commutative local ringA containing a field introduced by G. Lyubeznik in 1993 (Finiteness properties of local cohomology modules, Invent. Math. 113, 41– 55). We treat the cases dim(A) equal to zero, one and two, thereby answering in the negative a question raised in Lyubeznik’s paper. In fact, we will show that λp,i(A) has in the two...
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Let A be a d-dimensional local ring containing a field. We will prove that the highest Lyubeznik number λd,d(A) (defined in [5]) is equal to the number of connected components of the Hochster-Huneke graph (defined in [2]) associated to B, where B = ̂̂ Ash is the completion of the strict Henselization of the completion of A. This was proven by Lyubeznik in characteristic p > 0. Our statement and p...
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Let R = k[x1, ..., xn] be the polynomial ring in n independent variables, where k is a field. In this work we will study Bass numbers of local cohomology modules H I (R) supported on a squarefree monomial ideal I ⊆ R. Among them we are mainly interested in Lyubeznik numbers. We build a dictionary between the modules H I (R) and the minimal free resolution of the Alexander dual ideal I∨ that all...
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Let X be an arbitrary projective scheme over a field k. Let A be the local ring at the vertex of the affine cone for some embedding ι : X →֒ P n k . G. Lyubeznik asked (in [15]) whether the integers λi,j(A) (defined in [14]), called the Lyubeznik numbers of A, depend only on X, but not on the embedding. In this paper, we make a big step toward a positive answer to this question by proving that i...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05755-5