Waring decompositions of the product of two quadrics: the small rank cases
Authors
Meghana Bhat
Enrico Carlini
Saipriya Dubey
Shreedevi K. Masuti
Abstract
In this paper we study forms of the type $(x_1^2+ \cdots +x_m^2)(y_1^2+ \cdots+y_n^2)$ using projections. For $m=1, m=2$, and for any $n$ we describe: the forbidden locus, the structure and the Hilbert function of all minimal apolar sets. In particular, we show that every minimal apolar ideal has the same Hilbert function. For $m,n \geq 3,$ we provide new lower and upper bounds for the Waring rank.
