Dualité et comparaison pour les complexes de de Rham logarithmiques par rapport aux diviseurs libres

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 of the characteristic cycle of the D-module of meromorphic functions with respect to f , due to Àlvarez Montaner, García López and Zarzuela.

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“…f = (xz + y)(x 4 + y 5 + xy 4 ) (see [8]). In [5] the authors prove that the divisor defined by f in A 3 C is not of Spencer type. …”

Section: Remark 22 If Annmentioning

confidence: 98%

Localization at hyperplane arrangements: Combinatorics and D-modules

2007

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“…Ucha-Enríquez began work on this problem in [10] & [11], and they obtained a characterization for free divisors of Spencer type [12]. For a general free divisor, we have the following generalization 6 due to F.J. Calderón-Moreno and L. Narváez-Macarro [8]:…”

Section: A Differential Characterization Of Lct(d)mentioning

confidence: 99%

“…On the other hand, the complex Ω x 2 )(x 1 + x 2 x 3 ) = 0 is free but not of Spencer type (see [8], §5).…”

Section: Onmentioning

confidence: 99%

“…A key point in the proofs of Theorems 2.3 and 2.1 is the relationship between the duals of any integral logarithmic connection over the base ring D X and V D 0 (D X ) (see [11]; [8], §3). In particular, the holonomic D X -modules…”

Section: The Natural Morphismmentioning

confidence: 99%

“…Thus, the problem is now to find (geometrical) criteria on a free divisor to be of Spencer type (see [8], §5). The only known condition is to be a Koszul-free divisor (see [4] …”

Section: Onmentioning

confidence: 99%

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