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arXiv · 2004.01445

Cox rings of algebraic stacks

Andreas Hochenegger·Elena Martinengo·Fabio Tonini
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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.

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Andreas Hochenegger, Elena Martinengo, Fabio Tonini. 2024-01-02. Cox rings of algebraic stacks. https://doi.org/10.2422/2036-2145.202106_004

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