The variety of polar simplices II

Abstract

We discuss the space $VPS(Q,H)$ of ideals with Hilbert function $H=(1,n,n,\dots )$ that are apolar to a full rank quadric $Q$. We prove that its components of saturated ideals are closely related to the locus of Gorenstein algebras and to the Slip component in border apolarity. We also point out an important error in~[RS] and provide the necessary corrections.

version 2, final, to appear in Experimental Math