TWO-DIMENSIONAL NEIGHBORHOODS OF ELLIPTIC CURVES: FORMAL CLASSIFICATION AND FOLIATIONS

被引：6

作者：

Loray, Frank ^{[1
]}

Thom, Olivier ^{[1
]}

Touzet, Frederic ^{[1
]}

机构：

[1] Univ RENNES, CNRS, IRMAR UMR 6625, F-35000 Rennes, France

来源：

MOSCOW MATHEMATICAL JOURNAL | 2019年 / 19卷 / 02期

关键词：

Elliptic curves; formal neighborhoods; foliations; MAPPINGS;

D O I：

10.17323/1609-4514-2019-19-2-357-392

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：357 / 392

页数：36