On the -theory of smooth toric DM stacks
LA Borisov, RP Horja - arXiv preprint math/0503277, 2005 - arxiv.org
arXiv preprint math/0503277, 2005•arxiv.org
… In this paper we calculate the Grothendieck K-theory rings of coherent sheaves on
smooth toric Deligne-Mumford stacks. These stacks, which generalize the notion of a
smooth toric variety, have been defined in [BCS]. … We find that the Grothendieck group of
a smooth toric Deligne-Mumford stack PΣ is generated by classes of invertible sheaves, and
we find the generators of the ideal of relations satisfied by these sheaves. In the reduced
case K0(PΣ) is generated by the classes Ri of the invertible sheaves Li which correspond to …
smooth toric Deligne-Mumford stacks. These stacks, which generalize the notion of a
smooth toric variety, have been defined in [BCS]. … We find that the Grothendieck group of
a smooth toric Deligne-Mumford stack PΣ is generated by classes of invertible sheaves, and
we find the generators of the ideal of relations satisfied by these sheaves. In the reduced
case K0(PΣ) is generated by the classes Ri of the invertible sheaves Li which correspond to …
We explicitly calculate the Grothendieck -theory ring of a smooth toric Deligne-Mumford stack and define an analog of the Chern character. In addition, we calculate -theory pushforwards and pullbacks for weighted blowups of reduced smooth toric DM stacks.
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