English
Resolution of foliated varieties by torus actions
Multi angle
Auteurs : Wlodarczyk , Jaroslaw (Auteur de la Conférence)
CIRM (Editeur )
14E15 - Global theory and resolution of singularities
14F40 - de Rham cohomology
57S25 - Groups acting on specific manifolds
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3267/Slides/Wlodarczyk.pdf
CIRM (Editeur )
Loading the player...
|
Résumé :
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
Codes MSC : 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
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3267/Slides/Wlodarczyk.pdf
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 14/02/2025 Date de captation : 27/01/2025 Sous collection : Research School arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 00:52:54 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01_27_Wlodarczyk.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : Logarithmic and non-archimedean methods in Singularity Theory - Thematic Month Week 1 / Méthodes logarithmiques et non-archimédiennes en théorie des singularités - Mois thématique semaine 1Organisateurs de la rencontre : Fantini, Lorenzo ; Pełka, Tomasz ; Pichon, Anne ; Rond, Guillaume Dates : 27/01/2025 - 31/01/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3267.html
Données de citation
DOI : 10.24350/CIRM.V.20295203Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Semialgebraic Whitney partition of unity / Auteur de la Conférence Valette, Anna.
- [Multi angle] Semi-homogeneous bundles, Fourier-Mukai transforms, and tropicalization / Auteur de la Conférence Ulirsch, Martin.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 3 / Auteur de la Conférence Popescu-Pampu, Patrick.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - lecture 2 / Auteur de la Conférence Popescu-Pampu, Patrick.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 1 / Auteur de la Conférence Popescu-Pampu, Patrick.
- [Multi angle] Specialization techniques and stable rationality - Lecture 3 / Auteur de la Conférence Ottem, John Christian.
- [Multi angle] Specialization techniques and stable rationality - Lecture 2 - the motivic volume formula of Nicaise-Shinder / Auteur de la Conférence Ottem, John Christian.
- [Multi angle] Specialization techniques and stable rationality - Lecture 1 / Auteur de la Conférence Ottem, John Christian.
- [Multi angle] Piecewise linear geometry and spaces of valuations / Auteur de la Conférence Loeser, François.
- [Multi angle] A universal motivic invariant of birational maps / Auteur de la Conférence Lin, Hsueh-Yung.
- [Multi angle] Nash blowup fails to resolve singularities in dimensions four and higher / Auteur de la Conférence Leyton-Álvarez, Maximiliano.
- [Multi angle] A singular path through toric geometry / Auteur de la Conférence Gonzalez Perez, Pedro Daniel.
- [Multi angle] Teissier singularities / Auteur de la Conférence Mourtada, Hussein.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 3 / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 2 / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 1 / Auteur de la Conférence Forey, Arthur.
- [Multi angle] Motivic Milnor fibre and logarithmic geometry / Auteur de la Conférence Fichou, Goulwen.
- [Multi angle] Generic theta divisors / Auteur de la Conférence Budur, Nero.
- [Multi angle] The KSBA moduli space of stable log Calabi-Yau surfaces / Auteur de la Conférence Argüz, Hülya.
Bibliographie
- 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
Imagette Video
