# Moscow Mathematical Journal

Volume 19, Issue 2, April–June 2019 pp. 357–392.

Two-Dimensional Neighborhoods of Elliptic Curves: Formal Classification and Foliations

**Authors**:
Frank Loray (1), Olivier Thom (1), and Frédéric Touzet (1)

**Author institution:**(1) Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France

**Summary: **

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 for each formal model, we show that the
corresponding moduli space is infinite dimensional.

2010 Math. Subj. Class. 32G13, 37F75, 34M40.

**Keywords:**Elliptic curves, formal neighborhoods, foliations.

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