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 Title Localization at hyperplane arrangements: combinatorics and D-modules Author(s) Jose Alvarez-Montaner, Francisco Jesus Castro-Jimenez, Jose Maria Ucha-Enriquez Type Article in Journal Abstract We describe an algorithm for deciding whether the annihilating ideal of the meromorphic function $\frac{1}{f}$, where $f=0$ defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is based on a comparison of two characteristic cycles and uses a combinatorial description of the characteristic cycle of the $\scr D$-module of meromorphic functions with respect to $f$, due to J. Alvarez Montaner, R. GarciÂ­a Lopez and S. Zarzuela Armengou. We use Groebner bases in D-module theory to describe the characteristic cycle of a logarithmic D-module. ISSN 0021-8693 Language English Journal J. Algebra Volume 316 Number 2 Pages 662--679 Year 2007 Edition 0 Translation No Refereed No
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