On the $K$-theory of smooth toric DM stacks

Abstract

We explicitly calculate the Grothendieck $K$-theory ring of a smooth toric Deligne-Mumford stack and define an analog of the Chern character. In addition, we calculate $K$-theory pushforwards and pullbacks for weighted blowups of reduced smooth toric DM stacks.

arXiv comment28 pages, LaTeX

Cited by in corpus (13)

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• Quantum Cohomology and Periods
• The Crepant Transformation Conjecture for Toric Complete Intersections
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• The Grothendieck and Picard groups of a complete toric DM stack
• Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
• Quantum $K$-theory of toric varieties, level structures, and 3d mirror symmetry
• A note on toric Deligne-Mumford stacks
• Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system
• Frobenius morphisms and derived categories on two dimensional toric Deligne-Mumford stacks
• On the K-theory of Toric Stack Bundles
• Note on the Bondal-Orlov Functors for Toric DM Stacks