Forms with a unique representation as a sum of powers of linear forms

Rok, strany: 2005, 33 - 39

We consider forms of degree $dgeqslant 3$ over an algebraically closed field of characteristic $0$ which have a representation $f=l₁^d+…+l_r^d$, where $l_i$ are non-zero, projectively different linear forms in $n$ variables. Using some properties of $d$-independence we show that such a representation is unique provided that $f$ is non-degenerate and $dgeqslant 2lceil r-((n) / (2)) ceil +1$. We also show uniqueness of representation of a non-degenerate, indecomposable form of dimension $ngeqslant 4$ being a sum of $n+1$ powers of linear forms.

ISO 690:

Chlebowicz, A., Wołowiec-Musiał, M. 2005. Forms with a unique representation as a sum of powers of linear forms. In Tatra Mountains Mathematical Publications, vol. 32, no.3, pp. 33-39. 1210-3195.

APA:

Chlebowicz, A., Wołowiec-Musiał, M. (2005). Forms with a unique representation as a sum of powers of linear forms. Tatra Mountains Mathematical Publications, 32(3), 33-39. 1210-3195.