Claremont Topology Seminar: Reginald Anderson (CMC)

Title: Cellular resolutions of the diagonal and exceptional collections for toric Deligne-Mumford stacks

Abstract: Beilinson gave a resolution of the diagonal for complex projective space which yields a strong, full exceptional collection of line bundles. Bayer-Popescu-Sturmfels generalized Beilinson’s result to a cellular resolution of the diagonal for what they called “unimodular” toric varieties (a more restrictive condition than being smooth), which can also be extended to smooth toric varieties and global quotient toric DM stacks of a smooth toric variety by a finite abelian group, if we allow our resolution to have cokernel which is supported only along the vanishing of the irrelevant ideal. Here we show implications for exceptional collections of line bundles and a positive example for the modified King’s conjecture by giving a strong, full exceptional collection of line bundles on a smooth, non-unimodular nef-Fano complete toric surface.