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Non-holonomic simple $\mathcal D$-modules over complete intersections


Author: S. C. Coutinho
Journal: Proc. Amer. Math. Soc. 131 (2003), 83-86
MSC (2000): Primary 16S32; Secondary 37F75
Published electronically: May 9, 2002
MathSciNet review: 1929026
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Abstract: We show that if $X$ is a complex affine algebraic variety whose projective closure is a smooth complete intersection of dimension $n \geq 3$, then there exist non-holonomic simple ${\mathcal D}(X)$-modules of dimension $n+1$.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-02-06497-3
Keywords: Module, ring of differential operators
Received by editor(s): April 3, 2001
Received by editor(s) in revised form: August 22, 2001
Published electronically: May 9, 2002
Additional Notes: The author thanks Alcides Lins Neto and Luís Gustavo Mendes for many helpful conversations. During the preparation of this paper the author received financial support from CNPq and PRONEX (commutative algebra and algebraic geometry).
Communicated by: Martin Lorenz
Article copyright: © Copyright 2002 American Mathematical Society