Tohoku Mathematical Journal
2008
September
SECOND SERIES VOL. 60, NO. 3

Tohoku Math. J.
60 (2008), 441-458

Title A NOTE ON TORIC DELIGNE-MUMFORD STACKS

Author Fabio Perroni

(Received July 4, 2007, revised March 11, 2008)
Abstract. We give a new description of the data needed to specify a morphism from a scheme to a toric Deligne-Mumford stack. The description is given in terms of a collection of line bundles and sections which satisfy certain conditions. As applications, we characterize any toric Deligne-Mumford stack as a product of roots of line bundles over the rigidified stack, describe the torus action, describe morphisms between toric Deligne-Mumford stacks with complete coarse moduli spaces in terms of homogeneous polynomials, and compare two different definitions of toric stacks.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 14A20.

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