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Resolution of foliated varieties by torus actions
Multi angle
Authors : Wlodarczyk , Jaroslaw (Author of the conference)
CIRM (Publisher )
14E15 - Global theory and resolution of singularities
14F40 - de Rham cohomology
57S25 - Groups acting on specific manifolds
Additional resources :
https://www.cirm-math.fr/RepOrga/3267/Slides/Wlodarczyk.pdf
CIRM (Publisher )
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Abstract :
The resolution of singular foliations on analytic manifolds and algebraic varieties is a notoriously challenging problem, with only a few known partial results. In characteristic zero, we construct principalization of ideals on smooth foliated varieties. As an application, we prove the desingularization of Darboux totally integrable foliations in arbitrary dimensions, including both rational and meromorphic Darboux foliations. Additionally, we show how to transform a generically transverse section into a fully transverse one. Our approach relies on torus actions and uses weighted cobordant blow-ups, and is closely related to the analogous method of resolution of singularities of varieties.This is joint work with Abramovich, Belotto, and Temkin.
Keywords : Resolution of varities; resolution of foliations; Torus actions; bitational geometry
MSC Codes : Keywords : Resolution of varities; resolution of foliations; Torus actions; bitational geometry
14E15 - Global theory and resolution of singularities
14F40 - de Rham cohomology
57S25 - Groups acting on specific manifolds
Additional resources :
https://www.cirm-math.fr/RepOrga/3267/Slides/Wlodarczyk.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/02/2025 Conference Date : 27/01/2025 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:52:54 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01_27_Wlodarczyk.mp4 
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Information on the Event
Event Title : Logarithmic and non-archimedean methods in Singularity Theory - Thematic Month Week 1 / Méthodes logarithmiques et non-archimédiennes en théorie des singularités - Mois thématique semaine 1Event Organizers : Fantini, Lorenzo ; Pełka, Tomasz ; Pichon, Anne ; Rond, Guillaume Dates : 27/01/2025 - 31/01/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3267.html
Citation Data
DOI : 10.24350/CIRM.V.20295203Cite this video as: Wlodarczyk , Jaroslaw (2025). Resolution of foliated varieties by torus actions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20295203 URI : http://dx.doi.org/10.24350/CIRM.V.20295203 |
See Also
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Bibliography
- ABRAMOVICH, Dan, TEMKIN, Michael, and WŁODARCZYK, Jarosław. Functorial embedded resolution via weighted blowings up. arXiv preprint arXiv:1906.07106, 2019. - https://doi.org/10.48550/arXiv.1906.07106
- ABRAMOVICH, Dan, DA SILVA, Andre Belotto, TEMKIN, Michael, and WŁODARCZYK Jarosław. Principalization on logarithmically foliated orbifolds, 2025 (in preparation) -
- WŁODARCZYK, Jarosław. Functorial resolution except for toroidal locus. Toroidal compactification. arXiv preprint arXiv:2007.13846, 2020. - https://doi.org/10.48550/arXiv.2007.13846
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