Tate Resolutions for Products of Projective Spaces
Algebraic Geometry
2018-04-30 v1
Abstract
We describe the Tate resolution of a coherent sheaf or complex of coherent sheaves on a product of projective spaces. Such a resolution makes explicit all the cohomology of all twists of the sheaf, including, for example, the multigraded module of twisted global sections, and also the Beilinson monads of all twists. Although the Tate resolution is highly infinite, any finite number of components can be computed efficiently, starting either from a Beilinson monad or from a multigraded module.
Keywords
Cite
@article{arxiv.1411.5724,
title = {Tate Resolutions for Products of Projective Spaces},
author = {David Eisenbud and Daniel Erman and Frank-Olaf Schreyer},
journal= {arXiv preprint arXiv:1411.5724},
year = {2018}
}