On the Lyubeznik numbers of a local ring

Walther, Uli

doi:10.1090/S0002-9939-00-05755-5

On the Lyubeznik numbers of a local ring
HTML articles powered by AMS MathViewer

by Uli Walther PDF

Proc. Amer. Math. Soc. 129 (2001), 1631-1634 Request permission

Abstract:

We collect some information about the invariants $\lambda _{p,i}(A)$ of a commutative local ring $A$ 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 $\lambda _{p,i}(A)$ has in the two-dimensional case a topological interpretation.

References

M. P. Brodmann and R. Y. Sharp, Local cohomology: an algebraic introduction with geometric applications, Cambridge Studies in Advanced Mathematics, vol. 60, Cambridge University Press, Cambridge, 1998. MR 1613627, DOI 10.1017/CBO9780511629204
Robin Hartshorne, Cohomological dimension of algebraic varieties, Ann. of Math. (2) 88 (1968), 403–450. MR 232780, DOI 10.2307/1970720
C. Huneke and G. Lyubeznik, On the vanishing of local cohomology modules, Invent. Math. 102 (1990), no. 1, 73–93. MR 1069240, DOI 10.1007/BF01233420
Gennady Lyubeznik, Finiteness properties of local cohomology modules (an application of $D$-modules to commutative algebra), Invent. Math. 113 (1993), no. 1, 41–55. MR 1223223, DOI 10.1007/BF01244301
J. Montaner. Characteristic cycles of local cohomology modules. JPAA, 150:1–25, 2000.
M. Mustaţǎ. Local cohomology at monomial ideals. Preprint, 1998.
U. Walther. Algorithmic Computation of Local Cohomology Modules and the Cohomological Dimension of Algebraic Varieties. J. Pure Appl. Alg., 139:303–321, 1999.
K. Yanagawa. Bass numbers of local cohomology modules with supports in monomial ideals. Preprint, 1999.