Cox rings of algebraic stacks
Algebraic Geometry
2024-01-04 v3
Abstract
We give a proper definition of the multiplicative structure of the following rings: the Cox ring of invertible sheaves on a general algebraic stack; and the Cox ring of rank one reflexive sheaves on a normal and excellent algebraic stack. We show that such Cox rings always exist and establish their (non-)uniqueness in terms of an Ext-group. Moreover, we compare our definition with the classical construction of a Cox ring on a variety. Finally, we give an application to the theory of Mori dream stacks.
Cite
@article{arxiv.2004.01445,
title = {Cox rings of algebraic stacks},
author = {Andreas Hochenegger and Elena Martinengo and Fabio Tonini},
journal= {arXiv preprint arXiv:2004.01445},
year = {2024}
}
Comments
23 pages, minor changes. Same content as published version