Two dimensional neighborhoods of elliptic curves: formal classification and foliations - Archive ouverte HAL Access content directly
Journal Articles Moscow Mathematical Journal Year : 2019

Two dimensional neighborhoods of elliptic curves: formal classification and foliations

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 discuss analytic equivalence and show, for each formal model, that the corresponding moduli space is infinite dimensional.
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Dates and versions

hal-01509317 , version 1 (16-04-2017)
hal-01509317 , version 2 (09-05-2017)
hal-01509317 , version 3 (29-08-2018)

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Cite

Frank Loray, Olivier Thom, Frédéric Touzet. Two dimensional neighborhoods of elliptic curves: formal classification and foliations. Moscow Mathematical Journal, 2019, 19 (2), pp.357-392. ⟨hal-01509317v3⟩
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