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arxiv: math/0402256 · v1 · submitted 2004-02-16 · 🧮 math.DS · math.CV

Modules formels locaux de feuilletages holomorphes

classification 🧮 math.DS math.CV
keywords formalformsdeformationequisingularfinitegiveindenttype
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We give a complete list of formal invariants for a large class of formal differential 1-forms $\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy$. \indent A $\hat{SL}$-equisingular deformation is an equireducible deformation which leaves invariant both the local formal types and the holonomy representation of the components of the exceptional divisor. We characterize the 1-forms with finite formal type (t.f.f), i.e. those which admit a semi-universal $\hat{SL}$-equisingular deformation, and we give an explicit combinatorial criterion of finiteness. \indent The set of 1-forms with finite formal type contains a dense open set (in the sense of Krull's topology)in the set of 1-forms of the second kind.

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