Frobenius Morphisms and Derived Categories on Two Dimensional Toric Deligne-Mumford Stacks

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 2-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. (C) 2013 Elsevier Inc. All rights reserved.