  Varieties of Sums of Powers describe the additive decompositions of an
homogeneous polynomial into powers of linear forms. Despite their long history,
going back to Sylvester and Hilbert, few of them are known for special degrees
and number of variables. In this paper we aim to understand a general
birational behaviour of VSP, if any. To do this we birationally embed these
varieties into Grassmannians and prove the rationality, unirationality or
rational connectedness of many of those in arbitrary degrees and number of
variables.

Algebraic Geometry