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Decomposition of D-modules over a hyperplane arrangement in the plane
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 48, no 2, 211-229 p.Article in journal (Refereed) Published
Abstract [en]

Let alpha(1), alpha(2),..., alpha(m) be linear forms defined on C-n and X = C-n\boolean OR(m)(i=1) V(alpha(i)), where V(alpha(i))={p is an element of C-n : alpha(i)(p)=0}. The coordinate ring O-X of X is a holonomic A(n)-module, where A(n) is the nth Weyl algebra and since holonomic A(n)-modules have finite length, O-X has finite length. We consider a "" twisted"" variant of this An- 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. Our main result is the computation of the number of decomposition factors of M-alpha(beta) and their description when n-2.

Place, publisher, year, edition, pages
2010. Vol. 48, no 2, 211-229 p.
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URN: urn:nbn:se:su:diva-49192DOI: 10.1007/s11512-009-0103-7ISI: 000280594800001OAI: diva2:377152
authorCount :2Available from: 2010-12-13 Created: 2010-12-13 Last updated: 2010-12-13Bibliographically approved

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Abebaw, Tilahun
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