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This article is cited in 17 scientific papers (total in 17 papers)
Rigidity theorems for generic holomorphic germs of dicritic foliations and vector fields in $(\mathbb C^2,0)$
L. Ortiz-Bobadil'yaa, È. Rosales-Gonzáleza, S. M. Voroninb a National Autonomous University of Mexico
b Chelyabinsk State University
Abstract:
We consider the class $\mathcal V_{n+1}^d$ of dicritical germs of holomorphic vector fields in $(\mathbb C^2,0)$ with vanishing $n$-jet at the origin for $n\ge 1$. We prove, under some genericity assumptions, that the formal equivalence of two generic germs implies their analytic equivalence. A similar result is also established for orbital equivalence. Moreover, we give formal, orbitally formal, and orbitally analytic classifications of generic germs in $\mathcal V_{n+1}^d$ up to a change of coordinates with identity linear part.
Key words and phrases:
Dicritic foliations, dicritic vector fields, rigidity, formal equivalence, analytic equivalence.
Received: March 6, 2003
Citation:
L. Ortiz-Bobadil'ya, È. Rosales-González, S. M. Voronin, “Rigidity theorems for generic holomorphic germs of dicritic foliations and vector fields in $(\mathbb C^2,0)$”, Mosc. Math. J., 5:1 (2005), 171–206
Linking options:
https://www.mathnet.ru/eng/mmj190 https://www.mathnet.ru/eng/mmj/v5/i1/p171
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