Moscow Mathematical Journal

Volume 23, Issue 4, October–December 2023 pp. 545–558.

Fibered Toric Varieties

Authors: Askold Khovanskii (1) and Leonid Monin (2)
Author institution:(1) Department of Mathematics, University of Toronto, Toronto, Canada;
Moscow Independent University, Moscow, Russia.
(2) Institute of Mathematics, EPFL, Lausanne, Switzerland.

Summary:

A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class of fibered toric varieties. Then we use them to illustrate some known and conjectural results on topology and intersection theory of general toric variety bundles. Finally, using the language of fibered toric varieties, we compute the equivariant cohomology rings of smooth complete toric varieties.

2020 Math. Subj. Class. Primary: 14M25, 52B20; Secondary: 14C17, 14N10.

Keywords: Toric varieties, toric variety bundles, Newton polyhedra.

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