Directions of analytic discs attached to generic manifolds of finite type
The authors present an algorithmic construction of a certain finite- dimensional family of analytic discs attached to a generic manifold \(M\) of finite type in \(\mathbb{C}^ N\) allowing to determine a direction of wedge extendibility for all CR-functions on \(M\) near a point, thus completing the existence results obtained by \textit{A. E. Tumanov} [Math. USSR, Sb. 64, No. 1, 129-140 (1989); translation from Mat. Sb., Nov. Ser. 136(178), No. 1(5), 128-139 (1988; Zbl 0692.58005)] and the authors' previous results [Invent. Math. 101, No. 1, 45-56 (1990; Zbl 0712.32009)]. The same type of construction gives a family of analytic discs whose boundaries cover the generic manifold \(M\). The anisotropic wedge constructed in section 7 is a more natural region of extendibility for higher codimensions.
scientific article; zbMATH DE number 704498