A. Hochenegger, E. Martinengo

Mori Dream Stacks

Mathematische Zeitschrift, 280(3):1185-1202, 2015.
DOI: 10.1007/s00209-015-1472-1

Abstract. We propose a generalisation of Mori dream spaces to stacks. We show that this notion is preserved under root constructions and taking abelian gerbes. Unlike the case of Mori dream spaces, such a stack is not always given as a quotient of the spectrum of its Cox ring by the Picard group. We give a criterion when this is true in terms of Mori dream spaces and root constructions. Finally, we compare this notion with that of smooth toric Deligne-Mumford stacks.

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