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

Ryo Okawa; Hokuto Uehara

doi:10.1016/j.aim.2013.04.023

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

Ryo Okawa^*, Hokuto Uehara

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 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 language	English
Pages (from-to)	241-267
Number of pages	27
Journal	Advances in Mathematics
Volume	244
DOIs	https://doi.org/10.1016/j.aim.2013.04.023
Publication status	Published - 2013 Sept
Externally published	Yes

Keywords

Derived category
Full strong exceptional collection
Toric stack

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.aim.2013.04.023

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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.",

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AU - Okawa, Ryo

AU - Uehara, Hokuto

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AB - 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.

KW - Derived category

KW - Full strong exceptional collection

KW - Toric stack

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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