An infinitesimal study of secant space divisors Original Research Article

For a linear system gdn we define the subscheme Vee − f of the symmetric product C(e) parametrizing e-secant (e − f − 1)-space-divisors. For an element E of Vee − f we study the Zariski-tangent space. We give a description of this tangent space in terms of intersections with hyperplanes and quadrics. In particular, we are able to give an easy formula for the dimension of that tangent space for the case of secant line divisors. This completely solves a problem studied in our earlier paper [3]. In the appendix some of the results in Coppensʹ article are given natural interpretations in terms of local properties of subschemes of Grassmannians, such that these subschemes parametrize e-secant (e − f − 1)-planes.