Formal classication of two-dimensional neighborhoods of genus g $\ge$ 2 curves with trivial normal bundle

Abstract

In this paper we study the formal classication of two-dimensional neighborhoods of genus g $\ge$ 2 curves with trivial normal bundle. We first construct formal foliations on such neighborhoods with holonomy vanishing along many loops, then give the formal/analytic classication of neighborhoods equipped with two foliations, and finally put this together to obtain a description of the space of neighborhoods up to formal equivalence.