Arrondo Esteban, EnriqueBernadi, Alessandra2023-06-202023-06-2020110022-4049http://dx.doi.org10.1016/j.jpaa.2010.04.008https://hdl.handle.net/20.500.14352/42079The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneous polynomials of degree d in n + 1 variables on an algebraically closed field, called Split(d)(P(n)), with the Grassmannian of (n - 1)-dimensional projective subspaces of P(n+d-1). We compute the dimension of some secant varieties to Split(d)(P(n)). Moreover by using an invariant embedding of the Veronese variety into the Plucker space, we are able to compute the intersection of G(n - 1, n + d - 1) with Split(d)(P(n)), some of its secant varieties, the tangential variety and the second osculating space to the Veronese variety.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022404910000824restricted access514512Secant varietiesGrassmann varietiesGeometría diferencialÁlgebra1204.04 Geometría Diferencial1201 Álgebra