Abstract
For any vector bundle V on a toric Deligne–Mumford stack \({\mathcal X}\) the formalism of Edidin et al. (Ann K-theory 1(1):85–108, 2016) defines two inertial products \(\star _{V^{+}}\) and \(\star _{V^{-}}\) on the Chow group of the inertia stack. We give an explicit presentation for the integral \(\star _{V^+}\) and \(\star _{V^-}\) 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 \(V = 0\). 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.
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Research of the Dan Edidin partially supported by Simons Collaboration Grant 315460.
