An isotypic Kronecker web is a family of corank m foliations ${\left\{{ℱ}_t\right\}}_{t\in ℝP^1}$ such that the curve of annihilators t ↦ (T x F t)⊥ ∈ Grm(T x* M) is a rational normal curve in the Grassmannian Grm(T x*M) at any point x ∈ M. For m = 1 we get Veronese webs introduced by I. Gelfand and I. Zakharevich [Gelfand I.M., Zakharevich I., Webs, Veronese curves, and bi-Hamiltonian systems, J. Funct. Anal., 1991, 99(1), 150–178]. In the present paper, we consider the problem of local classification of isotypic Kronecker webs...

The webs have been studied mainly locally, near regular points (see a short list of references on the topic in the bibliography). Let d be an integer ≥ 1. A d-web on an open set U of ℂ² is a differential equation F(x,y,y’) = 0 with $F(x,y,y^{\text{'}})={\sum }_{i=0}^d{a}_i(x,y){\left(y^{\text{'}}\right)}^{d-i}$, where the coefficients $a_i$ are holomorphic functions, a₀ being not identically zero. A regular point is a point (x,y) where the d roots in y’ are distinct (near such a point, we have locally d foliations mutually transverse to each other, and caustics appear through...