On the variety parametrizing completely decomposable polynomials
نویسندگان
چکیده
The 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 Splitd(P ), with the Grassmannian of n−1 dimensional projective subspaces of P. We compute the dimension of some secant varieties to Splitd(P ) and find a counterexample to a conjecture that wanted its dimension related to the one of the secant variety to G(n−1, n+d−1). Moreover by using an invariant embedding of the Veronse variety into the Plücker space, we are able to compute the intersection of G(n−1, n+d−1) with Splitd(P ), some of its secant variety, the tangential variety and the second osculating space to the Veronese variety.
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