CIRM - Videos & books Library - MMP & foliations on 3-folds : applications

Virtualconference

Auteurs : Svaldi, Roberto (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : I will explain how the recent developments in the theory of birational geometry of rank 2 foliations on 3-folds have find quite a few applications in the study of the structure of such foliations and their singularities.
In this talk that is a complement to the course of Cascini and Spicer, but which will be self-contained, I shall briefly explain why the MMP terminates and then proceed to illustrate a few applications of these techniques, e.g., to the classification of canonical singularities, to the study of adjunction theory, and to the study of hyperbolicity properties of foliated 3-folds.
The work is in collaboration with Calum Spicer.

Keywords : holomorphic foliations; minimal model program; singularities; separatrices; hyperbolicity

Codes MSC :
14E30 - Minimal model program (Mori theory, extremal rays)
32S65 - Singularities of holomorphic vector fields and foliations
37F75 - Holomorphic foliations and vector fields

Informations sur la Vidéo

Réalisateur :

Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-05-28_Svaldi.mp4

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 feuilletages
Organisateurs 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.19639303
Citer cette vidéo: Svaldi, Roberto (2020). MMP & foliations on 3-folds : applications. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19639303
URI : http://dx.doi.org/10.24350/CIRM.V.19639303

Voir aussi

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[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.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 4 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 3 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 1 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Complete holomorphic vector fields and their singular points - lecture 2 / Auteur de la Conférence Guillot, Adolfo.
[Virtualconference] Fano foliations 3 - Classification of Fano foliations of large index - lecture 4 / Auteur de la Conférence Araujo, Carolina.
[Virtualconference] Fano foliations 1 - Definition, examples and first properties - lecture 2 / Auteur de la Conférence Araujo, Carolina.
[Virtualconference] MMP for co-rank1 foliations - lecture 2 / Auteur de la Conférence Spicer, Calum.
[Virtualconference] MMP for co-rank1 foliations - lecture 1 / Auteur de la Conférence Spicer, Calum.
[Virtualconference] MMP for foliations of rank one - lecture 2 / Auteur de la Conférence Cascini, Paolo.
[Virtualconference] An overview of the minimal model program - lecture 1 / Auteur de la Conférence Cascini, Paolo.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 3 / Auteur de la Conférence Touzet, Frédéric.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 2 / Auteur de la Conférence Touzet, Frédéric.
[Virtualconference] Codimension one foliation with pseudo-effective conormal bundle - lecture 1 / Auteur de la Conférence Touzet, Frédéric.
[Virtualconference] Holomorphic Poisson structures - lecture 4 / Auteur de la Conférence Pym, Brent.
[Virtualconference] Fano foliations 2 - Adjunction formula and applications - lecture 3 / Auteur de la Conférence Druel, Stéphane.
[Virtualconference] Fano foliations 0 - Algebraicity of smooth formal schemes and applications to foliations - lecture 1 / Auteur de la Conférence Druel, Stéphane.
[Virtualconference] Holomorphic Poisson structures - lecture 3 / Auteur de la Conférence Pym, Brent.
[Virtualconference] Holomorphic Poisson structures - lecture 2 / Auteur de la Conférence Pym, Brent.
[Virtualconference] Holomorphic Poisson structures - lecture 1 / Auteur de la Conférence Pym, Brent.

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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