Apolar: without differentiated poles; without apparent radiating processes applied to cells.
"Explanation of Terms Used in Entomology" by John. B. Smith
***
These varieties are studied via apolarity and syzygies.
Varieties of sums of powers
The apolar Artinian Gorenstein ring of a general cubic threefold 8.
Varieties of sums of powers
More generally we say that homogeneous forms f ∈ S and D ∈ T are apolar if f (D) = D(f ) = 0 (According to [Salmon 1885] the term was coined by Reye).
Varieties of sums of powers
In particular the socle of AF is 1-dimensional, and AF is indeed Gorenstein and is called the apolar Artinian Gorenstein ring of F ⊂ Pn .
Varieties of sums of powers
We call a subscheme Γ ⊂ ˇPn apolar to F , if the homogeneous ideal IΓ ⊂ F ⊥ ⊂ T .
Varieties of sums of powers
***