Cox rings and combinatorics - lecture 1 | Vidéo | Carmin.tv

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Cox rings and combinatorics - lecture 1

By Juergen Hausen

Appears in collection : Cox rings and applications / Anneaux de Cox et applications

The course starts with a reminder on toric varieties, which serve as an important and instructive example class for us. Then we switch to projective varieties with finitely generated divisor class group and study their Cox sheaf, Cox ring and the associated quotient presentation. We will focus in particular on the case of a finitely generated Cox ring. In this setting, we obtain natural embeddings into toric varieties, which in turn will lead to an explicit combinatorial approach to the geometry of the underlying variety. Specific examples, such as rational surfaces with $\mathbb{C^{²}}$-action, will be discussed in this context.

Information about the video

Date of recording 23/03/2026
Date of publication 03/04/2026
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20461303
Cite this video Hausen, Juergen (23/03/2026). Cox rings and combinatorics - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20461303
URL https://dx.doi.org/10.24350/CIRM.V.20461303

Domain(s)

Algebraic Geometry

Bibliography

BERCHTOLD, Florian et HAUSEN, Juergen. Cox rings and combinatorics. arXiv preprint math/0311105, 2003. - https://doi.org/10.48550/arXiv.math/0311105
HAUSEN, Jürgen. Cox rings and combinatorics II. arXiv preprint arXiv:0801.3995, 2008. - https://doi.org/10.48550/arXiv.0801.3995

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