Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages

Collection Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages

Organizer(s) Druel, Stéphane ; Pereira, Jorge Vitório ; Rousseau, Erwan

Date(s) 18/05/2020 - 22/05/2020

linked URL https://www.chairejeanmorlet.com/2251.html

00:00:00 / 00:00:00

22 28

MMP for co-rank1 foliations - lecture 1

By Calum Spicer

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.

Information about the video

Date of recording 05/05/2020
Date of publication 11/05/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19631703
Cite this video Spicer, Calum (05/05/2020). MMP for co-rank1 foliations - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19631703
URL https://dx.doi.org/10.24350/CIRM.V.19631703

Domain(s)

Algebraic Geometry

Bibliography

SPICER, Calum. Higher-dimensional foliated Mori theory. Compositio Mathematica, 2020, vol. 156, no 1, p. 1-38. - https://arxiv.org/abs/1709.06850
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

MSC codes

Document(s)

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