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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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https://hal.archives-ouvertes.fr/hal-01509317
Contributor : Frank Loray <>
Submitted on : Wednesday, August 29, 2018 - 9:37:20 AM
Last modification on : Friday, July 10, 2020 - 4:17:51 PM
Long-term archiving on: : Friday, November 30, 2018 - 12:36:43 PM

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  • HAL Id : hal-01509317, version 3
  • ARXIV : 1704.05214

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

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