On the Lyubeznik Numbers of a Local Ring

نویسنده

ULI WALTHER

چکیده

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-dimensional case a topological interpretation.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

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...

متن کامل

Lyubeznik 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 کامل

On Lyubeznik’s Invariants and the Vanishing of Local Cohomology

This paper contributes to the study of local cohomology and topological, in particular connectedness properties. Let I denote an ideal of a regular local ring (R,m) containing a field. There is a description of the Lyubeznik number λd,d(R/I), d = dimR/I, in terms of the topology of V (IR̂). In particular, λd,d(R/I) = 1 if and only if V (IR̂) is connected in codimension one. This provides an alter...

متن کامل