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An overview of the minimal model program - lecture 1
Virtualconference
Authors : Cascini, Paolo (Author of the conference)
CIRM (Publisher )
14E05 - Rational and birational maps
14E30 - Minimal model program (Mori theory, extremal rays)
37F75 - Holomorphic foliations and vector fields
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/2020-05-05_cascini_pdf_1.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/2020-05-05_cascini_pdf_1.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 08/05/2020 Conference Date : 05/05/2020 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:39:31 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-05-05_Cascini_Part1.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletagesEvent Organizers : Druel, Stéphane ; Pereira, Jorge Vitório ; Rousseau, Erwan Dates : 18/05/2020 - 22/05/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2251.html
Citation Data
DOI : 10.24350/CIRM.V.19631403Cite this video as: 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 |
See Also
- [Virtualconference] Hyperkähler structures on symplectic realizations of holomorphic Poisson surfaces / Author of the conference Mayrand, Maxence.
- [Virtualconference] MMP & foliations on 3-folds : applications / Author of the conference Svaldi, Roberto.
- [Virtualconference] Regular foliations on rationally connected manifolds / Author of the conference Figueredo, João Paulo.
- [Virtualconference] Boundedness of minimal partial du Val resolutions of canonical surface foliations / Author of the conference Chen, Yen-An.
- [Virtualconference] Topics on the Poisson varieties of dimension at least four / Author of the conference Okumura, Katsuhiko.
- [Virtualconference] A model-theoretic analysis of geodesic equations in negative curvature / Author of the conference Jaoui, Rémi.
- [Virtualconference] On symmetries of transversely projective foliations / Author of the conference Lo Bianco, Federico.
- [Virtualconference] Higher Ramanujan foliations / Author of the conference Jardim Da Fonseca, Tiago.
- [Virtualconference] Dynamics of Jouanolou foliation / Author of the conference Deroin, Bertrand.
Bibliography
- 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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