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Conormal varieties and characteristic varieties

Author(s): S. C. Coutinho; M. P. Holland; D. Levcovitz
Journal: Proc. Amer. Math. Soc. 128 (2000), 975-980.
MSC (1991): Primary 16S32; Secondary 13N10, 32C38
Posted: August 5, 1999
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Abstract: We show that the conormal variety of a quasihomogeneous hypersurface in ${\mathbb{C}}^{n}$, for $n\ge 4$, whose link is a $\mathbb{Q}$-homology sphere is not the characteristic variety of any ${\mathcal{D}}$-module.

References:

[Bo]
A. Borel et al., Algebraic $D$-modules (J. Coates and S. Helgason, eds.), Perspectives in Mathematics, 2, Academic Press, Orlando, 1987. MR 89g:32014

[Br]
E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math 2 (1966), 1-14. MR 34:6788

[BK]
J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig Conjecture and Holonomic Systems, Invent. Math. 64 (1981), 387-410. MR 83e:22020

[CL]
S.C. Coutinho and D. Levcovitz, Involutive varieties with smooth support, J. Algebra 192 (1997), 183-199. MR 98f:32010

[Co]
S.C. Coutinho, A primer of Algebraic $D$-modules, London Math. Soc. Student Texts 33, Cambridge University Press, 1995. MR 96j:32011

[Di]
A. Dimca, Singularities and topology of hypersurfaces, Springer, 1992. MR 94b:32058

[Ei]
D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Math. 150, Springer, 1995. MR 97a:13001

[Ge]
I.M. Gelfand, M.M. Kapranov and A.V. Zelevinsky, Discriminants, resultants and multidimensional determinants, Birhäuser, Boston-Basel-Berlin, 1994. MR 95e:14045

[Gi]
V. Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), 327-402. MR 87j:32030

[GM]
M. Goresky and R. MacPherson, Intersection homology II, Invent. Math. 72 (1983), 77-129. MR 84i:57012

[Gy]
A. Gyoja, Theory of prehomogenous vector spaces without regularity condition, Publ. RIMS, Kyoto University 27 (1991), 861-922. MR 93f:22018

[K]
M. Kashiwara, $B$-functions and holonomic systems (Rationality of roots of $b$-functions), Invent. Math. 38 (1976), 33-53. MR 55:3309

[LM]
D.T. Lê and Z. Mebkhout, Variétés caractéristiques et variétés polaires, C.R. Acad. Sc. Paris 296 (1983), 129-132. MR 84g:32018

[Ma]
B. Malgrange, Le polynôme de Bernstein d'une singularité isolée, Lect. Notes in Math. 459, Springer, 1975, pp. 98-119. MR 54:7485

[Ma2]
B. Malgrange, Motivations and introduction to the theory of ${\mathcal{D}}$-modules, Computer algebra and differential equations (E. Tournier, ed.), London Mathematical Society Lecture Note Series, 193, Cambridge University Press, Cambridge, 1994, pp. 3-20. MR 95h:32008

[Mi]
J. Milnor, Singular points of complex hypersurfaces, Annals of Mathematical Studies, 61, Princeton University Press, Princeton, 1968. MR 39:969

[SKKO]
M. Sato, M. Kashiwara, T. Kimura and T. Oshima, Micro-local analysis of prehomogeneous vector spaces, Invent. Math. 62 (1980), 117-179. MR 83g:32016

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Additional Information:

S. C. Coutinho
Affiliation: Departamento de Ciências da Computação, Universidade Federal do Rio de Janeiro, P.O. Box 68530, 21945-970 Rio de Janeiro, RJ, Brazil
Email: collier@impa.br

M. P. Holland
Affiliation: Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: m.holland@shef.ac.uk

D. Levcovitz
Affiliation: Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, P.O. Box 668, 13560-970 São Carlos, SP, Brazil
Email: lev@icmsc.sc.usp.br

DOI: 10.1090/S0002-9939-99-05137-0
PII: S 0002-9939(99)05137-0
Received by editor(s): August 15, 1996
Received by editor(s) in revised form: August 7, 1997 and June 2, 1998
Posted: August 5, 1999
Additional Notes: The first author was partially supported by CNPq (Brazil) during the preparation of this paper.
Communicated by: Ken Goodearl
Copyright of article: Copyright 2000, American Mathematical Society

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