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The orbifold cohomology ring of simplicial toric stack bundles. (English) Zbl 1231.14002
Summary: 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 P. Sankaran and V. Uma [Comment. Math. Helv. 78, No. 3, 540–554 (2003; Zbl 1050.14047); errata ibid. 79, 840–841 (2004)]. 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.

##### MSC:
 14A20 Generalizations (algebraic spaces, stacks) 14F40 de Rham cohomology and algebraic geometry
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##### References:
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