We describe the fundamental groups of ordered and unordered k-point sets in C^n generating an affine subspace of fixed dimension.

Let Fi h(k, n) be the ith ordered configuration space of all distinct points H1, . . . ,Hh in the Grassmannian Gr(k, n) of k-dimensional sub-spaces of Cn, whose sum is a subspace of dimension i. We prove that Fi h(k, n) is (when non empty) a complex submanifold of Gr(k, n)h of dimension i(n - i)...

We describe the fundamental groups of ordered and unordered k-point sets in Cn generating an affine subspace of fixed dimension.

Let Fi h(k, n) be the ith ordered configuration space of all distinct points H1, . . . ,Hh in the Grassmannian Gr(k, n) of k-dimensional sub- spaces of Cn, whose sum is a subspace of dimension i. We prove that Fi h(k, n) is (when non empty) a complex submanifold of Gr(k, n)h of dimension i(n -...