Translator Disclaimer
2017 On the integral cohomology ring of toric orbifolds and singular toric varieties
Anthony Bahri, Soumen Sarkar, Jongbaek Song
Algebr. Geom. Topol. 17(6): 3779-3810 (2017). DOI: 10.2140/agt.2017.17.3779

Abstract

We examine the integral cohomology rings of certain families of 2n–dimensional orbifolds X that are equipped with a well-behaved action of the n–dimensional real torus. These orbifolds arise from two distinct but closely related combinatorial sources, namely from characteristic pairs (Q,λ), where Q is a simple convex n–polytope and λ a labeling of its facets, and from n–dimensional fans Σ. In the literature, they are referred as toric orbifolds and singular toric varieties, respectively. Our first main result provides combinatorial conditions on (Q,λ) or on Σ which ensure that the integral cohomology groups H(X) of the associated orbifolds are concentrated in even degrees. Our second main result assumes these conditions to be true, and expresses the graded ring H(X) as a quotient of an algebra of polynomials that satisfy an integrality condition arising from the underlying combinatorial data. Also, we compute several examples.

Citation

Download Citation

Anthony Bahri. Soumen Sarkar. Jongbaek Song. "On the integral cohomology ring of toric orbifolds and singular toric varieties." Algebr. Geom. Topol. 17 (6) 3779 - 3810, 2017. https://doi.org/10.2140/agt.2017.17.3779

Information

Received: 20 December 2016; Revised: 22 March 2017; Accepted: 4 April 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791662
MathSciNet: MR3709660
Digital Object Identifier: 10.2140/agt.2017.17.3779

Subjects:
Primary: 14M25, 55N91, 57R18
Secondary: 13F55, 52B11

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
32 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.17 • No. 6 • 2017
MSP
Back to Top