منابع مشابه
Lyubeznik Numbers of Monomial Ideals
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...
متن کاملOn Lyubeznik Numbers of Projective Schemes
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...
متن کاملOn 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...
متن کاملLyubeznik Numbers of Local Rings and Linear Strands of Graded Ideals
In this work we introduce a new set of invariants associated to the linear strands of a minimal free resolution of a Z-graded ideal I ⊆ R = k[x1, . . . , xn]. We also prove that these invariants satisfy some properties analogous to those of Lyubeznik numbers of local rings. In particular, they satisfy a consecutiveness property that we prove rst for Lyubeznik numbers. For the case of squarefree...
متن کامل2 Josep Àlvarez Montaner and Gennady Lyubeznik
LetR = k[x1, . . . , xd] be the polynomial ring in d independent variables, where k is a field of characteristic p > 0. Let DR be the ring of k-linear differential operators of R and let f be a polynomial in R. In this work we prove that the localization R[ 1 f ] obtained from R by inverting f is generated as a DR-module by 1 f . This is an amazing fact considering that the corresponding charac...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2018
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rny126