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

Ryo Okawa, Hokuto Uehara

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)241-267
Number of pages27
JournalAdvances in Mathematics
Volume244
DOIs
Publication statusPublished - 2013 Sep
Externally publishedYes

Keywords

  • Derived category
  • Full strong exceptional collection
  • Toric stack

ASJC Scopus subject areas

  • Mathematics(all)

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