On toric schemes
Algebraic Geometry
2014-07-29 v2 Commutative Algebra
Abstract
Studying toric varieties from a scheme-theoretical point of view leads to toric schemes, i.e. "toric varieties over arbitrary base rings". It is shown how the base ring affects the geometry of a toric scheme. Moreover, generalisations of results by Cox and Mustata allow to describe quasicoherent sheaves on toric schemes in terms of graded modules. Finally, a toric version of the Serre-Grothendieck correspondence relates cohomology of quasicoherent sheaves on toric schemes to local cohomology of graded modules.
Cite
@article{arxiv.1107.2713,
title = {On toric schemes},
author = {Fred Rohrer},
journal= {arXiv preprint arXiv:1107.2713},
year = {2014}
}
Comments
updated references, minor corrections