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

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
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

References

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