Cox rings of algebraic stacks

• Autores: Andreas Hochenegger, Elena Martinengo, Fabio Tonini
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 24, Nº 4, 2023, págs. 2323-2349
• Idioma: inglés
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• Resumen

  • We give a proper definition of the multiplicative structure of the fol- lowing 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-)unique- ness 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.