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A note on toric Deligne-Mumford stacks


Perroni, F (2008). A note on toric Deligne-Mumford stacks. Tohoku Mathematical Journal, 60(3):441-458.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2008
Deposited On:09 Mar 2009 10:00
Last Modified:05 Apr 2016 13:05
Publisher:Tohoku Univ. Math. Inst. Sendai
ISSN:0040-8735
Publisher DOI:https://doi.org/10.2748/tmj/1223057738
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2453733
http://arxiv.org/abs/0705.3823v2

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