抄録
We discuss two kinds of compactifications of the configuration space of six points in the complex projective plane. One is Naruki's cross ratio variety and the other is a toric variety obtained from the regular triangulations of the product of two copies of the 2-simplex. The former admits a biregular action of the Weyl group of type E6. The latter admits a biregular action of S3×S3. The complement of the complex torus of the toric variety consists of normal crossing divisors. The action of S3×S3 leaves the set of normal crossing points invariant and decomposes this set into five orbits.
We explicitly show that the natural birational map between the two varieties is locally biregular around the normal crossing points of the toric variety and the corresponding points of the cross ratio variety. Utilizing this map, we study fundamental systems of solutions of the hypergeometric system E(3, 6) on the cross ratio variety which is a natural domain of definition of the hypergeometric functions of type (3, 6).
