X-ranks for embedded varieties and extensions of fields

Let X subset of P r be a projective embedded variety defined over a field K . Results relating maximum and generic X-rank of points of Pr(K) r ( K ) and Pr(L) r ( L ) are given, where L is a field containing K . Some of these results are algebraically closed for K and L . In other results (e.g. on the cactus rank), L is a finite extension of K .