Journal of the
Korean Mathematical Society JKMS

Let $U$, $V$ and $W$ be complex vector spaces of dimensions $3$, $3$ and $4$ respectively. The reductive algebraic group $G=PGL(U)\times PGL(V)\times PGL(W)$ acts linearly on the projective tensor product space ${\mathbb P}(U\otimes V\otimes W)$. In this paper, we show that the $G$-equivalence classes of the projective tensors are in one-to-one correspondence with the $PGL(3)$-equivalence classes of unordered configurations of six points on the projective plane.

Keywords: trilinear forms, cubic surfaces, configuration of six points on the plane

MSC numbers: 13D02, 14L30, 14M12, 14N20, 15A69