20 research outputs found
Exceptional collections on toric Fano threefolds and birational geometry
Bernardi and Tirabassi show the existence of full strong exceptional
collections consisting of line bundles on smooth toric Fano -folds under
assuming Bondal's conjecture, which states that the Frobenius push-forward of
the structure sheaf \mc O_X generates the derived category for
smooth projective toric varieties .
In this article, we show Bondal's conjecture for smooth toric Fano -folds
and also improve their result, using birational geometry.Comment: 6 figure
Frobenius morphisms and derived categories on two dimensional toric Deligne-Mumford stacks
For a toric Deligne-Mumford (DM) stack, we can consider a certain
generalization of the Frobenius endomorphism. For such an endomorphism on a
two-dimensional toric DM stack, we show that the push-forward of the structure
sheaf generates the bounded derived category of coherent sheaves on the toric
DM stack.
We also choose a full strong exceptional collection from the set of direct
summands of the push-forward in several examples of two dimensional toric DM
orbifolds.Comment: 32 page