2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62867We reconsider the classical problem of representing a finite number of forms of degree d in n+1 variables as sums of powers of linear forms. We define a geometric construct called a `grove', which, in a number of cases allows us to determine the dimension of the space of forms which can be so represented. We also present two new `exceptional' examples, where this dimension is less than what a naive parameter count would predict.LaTeX, 26 pagesAlgebraic Geometry14N15,51N35text