Frobenius morphisms and derived categories on two dimensional toric Deligne-Mumford stacks. (English) Zbl 1319.14021
Summary: For a toric Deligne-Mumford (DM) stack \(\mathcal X\), we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism \(F:\mathcal X\to \mathcal X\) on a 2-dimensional toric DM stack \(\mathcal X\), we show that the push-forward \(F_\ast \mathcal O_{\mathcal X}\) of the structure sheaf generates the bounded derived category of coherent sheaves on \(\mathcal X\).
We also choose a full strong exceptional collection from the set of direct summands of \(F_ \ast \mathcal O_ {\mathcal X}\) in several examples of two dimensional toric DM orbifolds \(\mathcal X\).
We also choose a full strong exceptional collection from the set of direct summands of \(F_ \ast \mathcal O_ {\mathcal X}\) in several examples of two dimensional toric DM orbifolds \(\mathcal X\).
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 14A20 | Generalizations (algebraic spaces, stacks) |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
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