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

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Authors : Svaldi, Roberto (Author of the conference)
CIRM (Publisher )

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Abstract : 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

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

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Film maker :

Hennenfent, Guillaume

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

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 feuilletages
Event 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.19639303
Cite this video as: 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

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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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