A Resolution of the Diagonal for Toric Deligne-Mumford Stacks
arXiv:2303.17497 · doi:10.1216/jca.2026.18.11
Abstract
Beilinson's resolution of the diagonal for complex projective space was generalized by Bayer-Popescu-Sturmfels for any unimodular toric variety. Here, we give a resolution of the diagonal for any smooth toric variety (viewed as a toric Deligne-Mumford stack) in families by deformation of the cellular complex of Bayer-Popescu-Sturmfels and show that the cokernel of this resolution gives the diagonal, modulo torsion from the irrelevant ideal. Furthermore, we give a resolution of the diagonal for a toric Deligne-Mumford stack associated to the global quotient of a smooth toric variety by a finite abelian group.
52 pages, 16 figures