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Decomposition factors of D-modules on hyperplane configurations in general position
Stockholm University, Faculty of Science, Department of Mathematics. Addis Ababa University, Ethiopia.
Stockholm University, Faculty of Science, Department of Mathematics.
2012 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 140, no 8, p. 2699-2711Article in journal (Refereed) Published
##### Abstract [en]

Let alpha(1), ... , alpha(m) be linear functions on C-n and X = C-n \ V(alpha), where alpha = Pi(m)(i=1) alpha(i) and V(alpha) = {p is an element of C-n : alpha(p) = 0}. The coordinate ring O-X = C[x](alpha) of X is a holonomic A(n)-module, where A(n) is the n-th Weyl algebra, and since holonomic A(n)-modules have finite length, O-X has finite length. We consider a twisted variant of this A(n)-module which is also holonomic. Define M-alpha(beta) to be the free rank 1 C[x](alpha)-module on the generator alpha(beta) (thought of as a multivalued function), where alpha(beta) = alpha(beta 1)(1) ... alpha(beta m)(m) and the multi-index beta = (beta(1), ... , beta(m)) is an element of C-m. It is straightforward to describe the decomposition factors of M-alpha(beta), when the linear functions alpha(1), ... , alpha(m) define a normal crossing hyperplane configuration, and we use this to give a sufficient criterion on beta for the irreducibility of M-alpha(beta), in terms of numerical data for a resolution of the singularities of V(alpha).

##### Place, publisher, year, edition, pages
2012. Vol. 140, no 8, p. 2699-2711
##### Keywords [en]
Hyperplane arrangements, D-module theory
Mathematics
##### Identifiers
ISI: 000306387400014OAI: oai:DiVA.org:su-80610DiVA, id: diva2:556879
##### Note

AuthorCount:2;

Available from: 2012-09-26 Created: 2012-09-25 Last updated: 2019-03-11Bibliographically approved

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