Varieties of simultaneous sums of power for binary forms

Abstract

The problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible decompositions is described. More generally the variety parametrizing the 0-dimensional schemes apolar to a set of generic binary forms is described. These results are applied to the study of particular secant spaces of rational curves.