The Chow rings and GKZ-decompositions for \(\mathbb{Q}\)-factorial toric varieties
type: Item
instance of: scholarly article
title: The Chow rings and GKZ-decompositions for \(\mathbb{Q}\)-factorial toric varieties
zbMATH Open document ID: 0799.14031
author: Hye Sook Park
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1993-06-17T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 52B20
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 52B40
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 203573
zbMATH Keywords: factorial toric variety
zbMATH Keywords: Chow ring
zbMATH Keywords: pull-back
zbMATH Keywords: push-forward
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225957
OpenAlex ID: W2061100354
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DOI: 10.2748/TMJ/1178225957
description: scientific article; zbMATH DE number 203573