The Chow rings and GKZ-decompositions for \(\mathbb{Q}\)-factorial toric varieties (Q1802567)

We define the Chow ring for a \(\mathbb{Q}\)-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. We also define the pull-back homomorphism and the push-forward homomorphism between the Chow rings in terms of the combinatorial structure of fans and a map of fans, and prove the projection formula without using algebro-geometric method. -- In the second part, we apply the GKZ-decomposition [cf. \textit{T. Oda} and the author, ``Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions'', Tôhoku Math. J., II. Ser. 43, No. 3, 375-399 (1991; Zbl 0782.52006)] to the \(\mathbb{Q}\)-factorial toric varieties and obtain some informations when the corresponding fans are confined to have one- dimensional cones within a fixed set.