Inertial Chow rings of toric stacks

Abstract

For any vector bundle $V$ on a toric Deligne-Mumford stack $\ix$ the formalism of \cite{EJK:16} defines two intertial 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 Boris-Chen-Smith \cite{BCS:05} and Jiang-Tsen \cite{JiTs:10} in the orbifold Chow ring case, which corresponds to $V=0$. We also describe an {\em asymptotic} product on the rational Chow group of the inertia stack obtained by letting the rank of the bundle $V$ go to infinity.

References in corpus (1)

• Logarithmic trace and orbifold products