Directions of Analytic Discs Attached to Generic Manifolds of Finite Type

In this paper, we construct a finite-dimensional family of analytic discs attached to a generic manifold M of finite type in CN. More precisely, we determine sufficiently many parameters to guarantee that the associated analytic discs sweep out an open wedge in CN. This construction, which is based on earlier work of Tumanov, gives an explicit algorithm for determining a wedge of extendibility for all CR functions on M near a point. We also define the notion of an anisotropic wedge, which is a more natural region of extendibility in higher codimension.