Examples of k-regular maps and interpolation spaces

A continuous map f:Cn→CN is k-regular if the image of any k distinct points spans a k-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev, to construct k-regular maps with small N, and only a few nontrivial examples are known so far. Applying tools from algebraic geometry we construct a 4-regular polynomial map C3→C11 and a 5-regular polynomial map C3→C14.