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arXiv · 1704.05214

Two dimensional neighborhoods of elliptic curves: formal classification and foliations

Frank Loray·Olivier Thom·Frédéric Touzet
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Abstract

We classify two dimensional neighborhoods of an elliptic curve C with torsion normal bundle, up to formal equivalence. The proof makes use of the existence of a pair (indeed a pencil) of formal foliations having C as a common leaf, and the fact that neighborhoods are completely determined by the holonomy of such a pair. We also discussanalytic equivalence and show, for each formal model, that the corresponding moduli space is infinite dimensional.

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Frank Loray, Olivier Thom, Frédéric Touzet. 2017-04-18. Two dimensional neighborhoods of elliptic curves: formal classification and foliations. https://arxiv.org/abs/1704.05214

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