7,331 research outputs found
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.Comment: 9 pages, accepted in Communications in Algebr
Generating functions associated to Frobenius algebras
We introduce a generating function associated to the homogeneous generators
of a graded algebra that measures how far is this algebra from being finitely
generated. For the case of some algebras of Frobenius endomorphisms we describe
this generating function explicitly as a rational function.Comment: 15 pages. Published in Linear Algebra App
PI theory for Associative Pairs
We extend the classical associative PI-theory to Associative Pairs, and in
doing so, we introduce related notions already present for algebras (and Jordan
systems) as the ones of PI-element and PI-ideal, extended centroid and central
closure
Some remarks on the Lp regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition
In this note we prove an end-point regularity result on the Lp integrability
of the second derivatives of solutions to non-divergence form uniformly
elliptic equations whose second derivatives are a priori only known to be
integrable. The main assumption on the elliptic operator is the Dini continuity
of the coefficients. We provide a counterexample showing that the Dini
condition is somehow optimal. We also give a counterexample related to the BMO
regularity of second derivatives of solutions to elliptic equations
Lyubeznik numbers of monomial ideals
We study Bass numbers of local cohomology modules supported on squarefree
monomial ideals paying special attention to Lyubeznik numbers. We build a
dictionary between local cohomology modules and minimal free resolutions that
allow us to interpret Lyubeznik numbers as the obstruction to the acyclicity of
the linear strands of the Alexander dual ideals. The methods we develop also
help us to give a bound for the injective dimension of the local cohomology
modules in terms of the dimension of the small support.Comment: 28 page
Computing the support of local cohomology modules
For a polynomial ring , we present a method to compute the
characteristic cycle of the localization for any nonzero polynomial that avoids a direct computation of as a -module. Based on this
approach, we develop an algorithm for computing the characteristic cycle of the
local cohomology modules for any ideal using the
\v{C}ech complex. The algorithm, in particular, is useful for answering
questions regarding vanishing of local cohomology modules and computing
Lyubeznik numbers. These applications are illustrated by examples of
computations using our implementation of the algorithm in Macaulay~2.Comment: 15 page
Addendum to "Frobenius and Cartier algebras of Stanley-Reisner rings" [J. Algebra 358 (2012) 162-177]
We give a purely combinatorial characterization of complete Stanley-Reisner
rings having principally generated (equivalently, finitely generated) Cartier
algebras.Comment: The main result restated in a cleaner way. 5 pages, 2 figures. To
appear in J. Algebr
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