Frobenius morphisms and derived categories on two dimensional toric Deligne-Mumford stacks

  • Ohkawa R
  • Uehara H
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Abstract

For a toric Deligne-Mumford (DM) stack X, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism F:X→X on a dimensional toric DM stack X, we show that the push-forward F*OX of the structure sheaf generates the bounded derived category of coherent sheaves on X .We also choose a full strong exceptional collection from the set of direct summands of F *OX in several examples of two dimensional toric DM orbifolds X. © 2013 Elsevier Ltd.

Author-supplied keywords

  • Derived category
  • Full strong exceptional collection
  • Toric stack

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Authors

  • Ryo Ohkawa

  • Hokuto Uehara

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