Über gewisse G-stabile Teilmengen in pojektiven Räumen.
Let F be a homogeneous polynomial of degree d in m + 1 variables defined over an algebraically closed field of characteristic 0 and suppose that F belongs to the sth secant variety of the d-uple Veronese embedding of into but that its minimal decomposition as a sum of dth powers of linear forms requires more than s summands. We show that if s ≤ d then F can be uniquely written as , where are linear forms with t ≤ (d-1)/2, and Q is a binary form such that with ’s linear forms and ’s forms...
Let be a uniruled projective manifold and let be a general point. The main result of [2] says that if the -degrees (i.e., the degrees with respect to the anti-canonical bundle of ) of all rational curves through are at least , then is a projective space. In this paper, we study the structure of when the -degrees of all rational curves through are at least . Our study uses the projective variety , called the VMRT at , defined as the union of tangent directions to the rational curves...