Generalized Lyubeznik numbers

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...

On 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...

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...

On generalized fuzzy numbers

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Addition two generalized fuzzy numbers