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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Residues of a Pfaff system relative to an invariant subscheme

Author(s): F. Sancho de Salas
Journal: Trans. Amer. Math. Soc. 352 (2000), 4019-4035.
MSC (2000): Primary 14B05, 14H20, 32S65; Secondary 57R20, 37C85, 57R30
Posted: April 21, 2000
MathSciNet review: 1695020
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Abstract | References | Similar articles | Additional information

Abstract:

In this paper we give a purely algebraic construction of the theory of residues of a Pfaff system relative to an invariant subscheme. This construction is valid over an arbitrary base scheme of any characteristic.


References:

[1]
M. F. Atiyah: Complex analytic connections in fibre bundles. Trans. Amer. Math. Soc. 85 (1957), pp. 181-207.MR 19:172c

[2]
C. Camacho and P. Sad: Invariant varieties through singularities of holomorphic vector fields. Annals of Math. 115 (1982), pp. 579-595.MR 83m:58062

[3]
B. Gmira: Une généralisation d'un théorème de C. Camacho et P. Sad relatif aus feuilletages holomorphes singuliers. Thèse de III ${}^{\text{ lq {e}me }}$ cycle, Lille (1984).

[4]
A. Grothendieck: Classes de Chern et représentations linéaires des groupes discrets. Dix esposés sur la cohomologie des schémas. North-Holland, (1968), pp. 215-305.MR 42:280

[5]
D. Lehmann and T. Suwa: Residues of holomorphic vector fields relative to singular invariant subvarieties. J. of Differential Geom. 42, 1995, 165-192.MR 96f:32064

[6]
D. Lehmann: Résidus des sous-variétés invariantes d'un feuilletage singulier. Ann. Inst. Fourier 41 (1991) pp. 211-258 (Bucarest). MR 92k:57054

[7]
A. Lins Neto: Algebraic solutions of polynomial differential equations and foliations in dimension two. Holomorphic Dynamics, Mexico 1986, Lecture Notes in Math. 1345 (1988) pp. 192-232.MR 90c:58142

[8]
A. Lins Neto: Complex codimension one foliations leaving a compact submanifold invariant. Dynamical Systems and Bifurcation Theory 1985, Pitman Research Notes in Mathematics Series 160, Longman Scientific and Technical, Harlow, New York (1987), pp. 295-317.MR 88m:57036

[9]
M. Soares: A note on algebraic solutions of foliations in dimension 2. Dynamical Systems 1990, Pitman Research Notes in Mathematics Series 285, Longman Scientific and Technical, Harlow, New York (1993), pp. 250-254.MR 94k:32054

[10]
T. Suwa: Indices of holomorphic vector fields relative to invariant curves on surfaces. Proc. Amer. Math. Soc. 123, 1995, 2989-2997.MR 95m:32054

[11]
T. Suwa: Residues of complex analytic foliation singularities. J. Math. Soc. Japan, 36, (1984) pp. 37-45.MR 85f:32016

[12]
T. Suwa: Residues of complex analytic foliations relative to singular invariant subvarieties. Proceedings of the International Seminar on Complex Geometry and Singularities, Beijing (1994) pp. 230-245. MR 98i:32053

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Additional Information:

F. Sancho de Salas
Affiliation: Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain
Email: fsancho@gugu.usal.es

DOI: 10.1090/S0002-9947-00-02559-9
PII: S 0002-9947(00)02559-9
Keywords: Residues, singularities, foliation
Received by editor(s): June 20, 1998
Posted: April 21, 2000
Copyright of article: Copyright 2000, American Mathematical Society




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