# Inertial Chow rings of toric stacks

Inertial Chow rings of toric stacks For any vector bundle V on a toric Deligne–Mumford stack $${\mathcal X}$$ X the formalism of Edidin et al. (Ann K-theory 1(1):85–108, 2016) defines two inertial products $$\star _{V^{+}}$$ ⋆ V + and $$\star _{V^{-}}$$ ⋆ V - on the Chow group of the inertia stack. We give an explicit presentation for the integral $$\star _{V^+}$$ ⋆ V + and $$\star _{V^-}$$ ⋆ V - Chow rings, extending earlier work of Borisov et al. (J Am Math Soc 18(1):193–215, 2005) and Jiang and Tseng (Math Z 264(1):225–248, 2010) in the orbifold Chow ring case, which corresponds to $$V = 0$$ V = 0 . We also describe an asymptotic product on the rational Chow group of the inertia stack obtained by letting the rank of the bundle V go to infinity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Manuscripta Mathematica Springer Journals

# Inertial Chow rings of toric stacks

, Volume 156 (4) – Nov 2, 2017
29 pages

/lp/springer_journal/inertial-chow-rings-of-toric-stacks-fkx09OppHn
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
ISSN
0025-2611
eISSN
1432-1785
D.O.I.
10.1007/s00229-017-0982-z
Publisher site
See Article on Publisher Site

### Abstract

For any vector bundle V on a toric Deligne–Mumford stack $${\mathcal X}$$ X the formalism of Edidin et al. (Ann K-theory 1(1):85–108, 2016) defines two inertial products $$\star _{V^{+}}$$ ⋆ V + and $$\star _{V^{-}}$$ ⋆ V - on the Chow group of the inertia stack. We give an explicit presentation for the integral $$\star _{V^+}$$ ⋆ V + and $$\star _{V^-}$$ ⋆ V - Chow rings, extending earlier work of Borisov et al. (J Am Math Soc 18(1):193–215, 2005) and Jiang and Tseng (Math Z 264(1):225–248, 2010) in the orbifold Chow ring case, which corresponds to $$V = 0$$ V = 0 . We also describe an asymptotic product on the rational Chow group of the inertia stack obtained by letting the rank of the bundle V go to infinity.

### Journal

Manuscripta MathematicaSpringer Journals

Published: Nov 2, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations