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Polyhedral divisors and torus actions of...

Langlois, Kevin...

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Polyhedral divisors and torus actions of complexity one over arbitrary fields by Langlois, Kevin ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	11-08-2023
Summary	We show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra associated to a polyhedral divisor changes when we extend the scalars. As another application, we provide a combinatorial description of affine $\mathbf{G}$-varieties of complexity one over a field, where $\mathbf{G}$ is a (not-nescessary split) torus, by using elementary facts on Galois descent. This class of affine $\mathbf{G}$-varieties is described via a new combinatorial object, which we call (Galois) invariant polyhedral divisor.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1207.0208

Citation

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AMA 11th EditionReferences

Langlois, Kevin. Polyhedral divisors and torus actions of complexity one over arbitrary fields. Australian National University. August 11, 2023. Accessed October 02, 2025. https://online.provdatabase.com/cite/15934

APA 7th EditionReferences

Langlois, Kevin. (2023). Polyhedral divisors and torus actions of complexity one over arbitrary fields. Australian National University. https://online.provdatabase.com/cite/15934

Chicago 17th EditionReferences

Langlois, Kevin. Polyhedral divisors and torus actions of complexity one over arbitrary fields. Australian National University. 2023. https://online.provdatabase.com/cite/15934

HarvardReferences

Langlois, Kevin. (2023). Polyhedral divisors and torus actions of complexity one over arbitrary fields. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/15934. (Accessed 02 October 2025).

Harvard AustraliaReferences

Langlois, Kevin, 2023, Polyhedral divisors and torus actions of complexity one over arbitrary fields, Australian National University, viewed 02 October 2025, <https://online.provdatabase.com/cite/15934>

MLA 9th EditionWorks Cited

Langlois, Kevin. Polyhedral divisors and torus actions of complexity one over arbitrary fields. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/15934.

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