Cross Ratio Varieties for Root Systems of Type $A$ and the Terada Model

Abstract

The notion of cross ratio varieties for root systems is introduced in [7]. Among others, in the case of the root system of type $A_{n+2}$, it was conjectured (cf. Conjecture 2.2 in [7]) that the corresponding cross ratio variety is isomorphic to the $n$-dimensional Terada model which is a natural compactification of the complement in ${\bf P}^n$ of the singular locus of the holonomic system of differential equations for the Appell-Lauricella hypergeometric function $F_D$. The purpose of this article is to prove this conjecture.