On the variety of sum of powers of certain complete intersection forms

Abstract

Let $F$ be a homogeneous polynomial (form). If the annihilator ideal $F^\perp$ is a complete intersection, then $F$ is called as a complete intersection form. For many complete intersection forms, we show that its minimal apolar ideal is a complete intersection and further we show that ${\rm VSP}(F)$ is irreducible and compute its dimension.