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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Foliations of multiprojective spaces and a conjecture of Bernstein and Lunts


Author: S. C. Coutinho
Journal: Trans. Amer. Math. Soc. 363 (2011), 2125-2142
MSC (2000): Primary 37F75, 16S32; Secondary 37J30, 32C38, 32S65
Published electronically: October 28, 2010
MathSciNet review: 2746677
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Abstract: We use foliations of multiprojective spaces defined by Hamiltonian functions on the underlying affine space to prove the three dimensional case of a conjecture of Bernstein and Lunts, according to which the symbol of a generic first-order differential operator gives rise to a hypersurface of the cotangent bundle which does not contain involutive conical subvarieties apart from the zero section and fibres of the bundle.


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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, Rio de Janeiro, Brazil – and – Programa de Engenharia de Sistemas e Computação, COPPE, Universidade Federaldo Rio de Janeiro, PO Box 68511, 21941-972 Rio de Janeiro, Rio de Janeiro, Brazil
Email: collier@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05230-4
PII: S 0002-9947(2010)05230-4
Keywords: Derivation, singularity, invariant variety, Hamiltonian, symplectic geometry, $\mathscr D$-module.
Received by editor(s): July 6, 2009
Published electronically: October 28, 2010
Additional Notes: The author wishes to thank Jorge Vitório Pereira for his help with section 4. The work on this paper was partially supported by a grant from CNPq.
Dedicated: To Israel Vainsencher on his 60th birthday
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.