English
An overview of the minimal model program - lecture 1
Virtualconference
Auteurs : Cascini, Paolo (Auteur de la Conférence)
CIRM (Editeur )
14E05 - Rational and birational maps
14E30 - Minimal model program (Mori theory, extremal rays)
37F75 - Holomorphic foliations and vector fields
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/2020-05-05_cascini_pdf_1.pdf
CIRM (Editeur )
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Résumé :
The goal of the Minimal Model Program (MMP) is to provide a framework in which the classification of varieties or foliations can take place. The basic strategy is to use surgery operations to decompose a variety or foliation into "building block” type objects (Fano, Calabi-Yau, or canonically polarized objects).
We first review the basic notions of the MMP in the case of varieties. We then explain work on realizing the MMP for foliations on threefolds (both in the case of codimension =1 and dimension =1 foliations). We explain and pay special attention to results such as the Cone and Contraction theorem, the Flip theorem and a version of the Basepoint free theorem.
Keywords : foliations; minimal model program
Codes MSC : We first review the basic notions of the MMP in the case of varieties. We then explain work on realizing the MMP for foliations on threefolds (both in the case of codimension =1 and dimension =1 foliations). We explain and pay special attention to results such as the Cone and Contraction theorem, the Flip theorem and a version of the Basepoint free theorem.
Keywords : foliations; minimal model program
14E05 - Rational and birational maps
14E30 - Minimal model program (Mori theory, extremal rays)
37F75 - Holomorphic foliations and vector fields
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/2020-05-05_cascini_pdf_1.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 08/05/2020 Date de captation : 05/05/2020 Sous collection : Research School arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 00:39:31 Audience : Researchers Download : https://videos.cirm-math.fr/2020-05-05_Cascini_Part1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletagesOrganisateurs de la rencontre : Druel, Stéphane ; Pereira, Jorge Vitório ; Rousseau, Erwan Dates : 18/05/2020 - 22/05/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2251.html
Données de citation
DOI : 10.24350/CIRM.V.19631403Citer cette vidéo: Cascini, Paolo (2020). An overview of the minimal model program - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19631403 URI : http://dx.doi.org/10.24350/CIRM.V.19631403 |
Voir aussi
- [Virtualconference] Hyperkähler structures on symplectic realizations of holomorphic Poisson surfaces / Auteur de la Conférence Mayrand, Maxence.
- [Virtualconference] MMP & foliations on 3-folds : applications / Auteur de la Conférence Svaldi, Roberto.
- [Virtualconference] Regular foliations on rationally connected manifolds / Auteur de la Conférence Figueredo, João Paulo.
- [Virtualconference] Boundedness of minimal partial du Val resolutions of canonical surface foliations / Auteur de la Conférence Chen, Yen-An.
- [Virtualconference] Topics on the Poisson varieties of dimension at least four / Auteur de la Conférence Okumura, Katsuhiko.
- [Virtualconference] A model-theoretic analysis of geodesic equations in negative curvature / Auteur de la Conférence Jaoui, Rémi.
- [Virtualconference] On symmetries of transversely projective foliations / Auteur de la Conférence Lo Bianco, Federico.
- [Virtualconference] Higher Ramanujan foliations / Auteur de la Conférence Jardim Da Fonseca, Tiago.
- [Virtualconference] Dynamics of Jouanolou foliation / Auteur de la Conférence Deroin, Bertrand.
Bibliographie
- SPICER, Calum. Higher-dimensional foliated Mori theory. Compositio Mathematica, 2020, vol. 156, no 1, p. 1-38. - https://doi.org/10.1112/S0010437X19007681
- CASCINI, Paolo et SPICER, Calum. MMP for co-rank one foliation on threefolds. arXiv preprint arXiv:1808.02711, 2018. - https://arxiv.org/abs/1808.02711
- SPICER, Calum et SVALDI, Roberto. Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds. arXiv preprint arXiv:1908.05037, 2019. - https://arxiv.org/abs/1908.05037
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