On Waring's problem for several homogeneous forms

Details On Waring's problem for several homogeneous forms On Waring's problem for several homogeneous forms

2001-12-12

arxiv.org/abs/math/0112110v1

Mathematics

Algebraic Geometry

LaTeX, 26 pages

Scientific paper

We 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.

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