The orbifold cohomology ring of simplicial toric stack bundles

Abstract

We introduce a new quotient construction of toric Deligne–Mumford stacks. We use this new construction to define toric stack bundles which generalize the construction of toric bundles by Sankaran and Uma [Comment. Math. Helv. 78 (2003) 540–554]. The orbifold Chow ring of such toric stack bundles is computed. We show that the orbifold Chow ring of the toric stack bundle and the Chow ring of its crepant resolution are fibres of a flat family, generalizing a result of Borisov–Chen–Smith.