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

 

Desingularizations of plane vector fields


Author: F. Cano
Journal: Trans. Amer. Math. Soc. 296 (1986), 83-93
MSC: Primary 14D05; Secondary 14B05, 32B30
MathSciNet review: 837799
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Abstract: The singularities of a plane vector field can be reduced under quadratic blowing ups. We describe a control method for the singularities of the vector field which works for ground fields of any characteristic and which has no essential obstruction for generalizing to higher dimensional cases.


References [Enhancements On Off] (What's this?)

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  • [7] Arno van den Essen, Reduction of singularities of the differential equation 𝐴𝑑𝑦=𝐵𝑑𝑥, Équations différentielles et systèmes de Pfaff dans le champ complexe (Sem., Inst. Rech. Math. Avancée, Strasbourg, 1975) Lecture Notes in Math., vol. 712, Springer, Berlin, 1979, pp. 44–59. MR 548142 (82m:34007)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0837799-3
PII: S 0002-9947(1986)0837799-3
Keywords: Vector field, reduction of singularities
Article copyright: © Copyright 1986 American Mathematical Society