2 Josep Àlvarez Montaner and Gennady Lyubeznik
نویسنده
چکیده
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 characteristic zero statement is very false.
منابع مشابه
Lyubeznik Table of Sequentially Cohen-macaulay Rings
We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are also provided depending on the deficiency modules of the ring.
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 کاملComputing the support of local cohomology modules
For a polynomial ring R = k[x1, ..., xn], we present a method to compute the characteristic cycle of the localization Rf for any nonzero polynomial f ∈ R that avoids a direct computation of Rf as a D-module. Based on this approach, we develop an algorithm for computing the characteristic cycle of the local cohomology modules H I (R) for any ideal I ⊆ R using the Čech complex. The algorithm, in ...
متن کاملLyubeznik 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 کاملLocalization at Hyperplane Arrangements: Combinatorics and D-modules
We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on the comparison of two characteristic cycles and uses a combinatorial description due to Àlvarez-Montaner, Garćıa–López and Zarzuela of the characteristic cycle of the D...
متن کامل