Cox rings and combinatorics - lecture 2 | Vidéo | Carmin.tv

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Cox rings and combinatorics - lecture 2

De Juergen Hausen

Apparaît dans la 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.

Informations sur la vidéo

Date de captation 23/03/2026
Date de publication 03/04/2026
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent, Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20461403
Citer cette vidéo Hausen, Juergen (23/03/2026). Cox rings and combinatorics - lecture 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20461403
URL https://dx.doi.org/10.24350/CIRM.V.20461403

Domaine(s)

Géométrie algébrique

Bibliographie

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

Codes MSC

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