Fibered Toric Varieties

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2023-11-03 DOI:10.17323/1609-4514-2023-23-4-545-558

Askold Khovanskii, Leonid Monin

引用次数: 0

Abstract

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.

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纤维环变种

如果一个环状变种可以表示为环状基上的纤维束总空间，并且具有环状纤维，那么这个环状变种就叫做纤维环状变种。有纤维的环状变分是环状变分束的一种特例。在本论文中，我们首先介绍了纤维环状变种。然后，我们用它们来说明关于一般环综束的拓扑学和交集理论的一些已知和猜想结果。最后，我们用纤维环综的语言计算光滑完整环综的等变同调环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.