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 $\mathrm{VSP}(F)$ is irreducible and compute its dimension.

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