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Specialization techniques and stable rationality - Lecture 2
the motivic volume formula of Nicaise-Shinder
Multi angle
Authors : Ottem, John Christian (Author of the conference)
CIRM (Publisher )
14E05 - Rational and birational maps
14E08 - Rationality questions
14T90 - Applications of tropical geometry
Additional resources :
https://www.cirm-math.fr/RepOrga/3267/Slides/Ottem_CIRM_slides_complete.pdf
CIRM (Publisher )
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Abstract :
The talks will be about the use of the motivic obstruction to stable rationality introduced by Nicaise–Shinder to the rationality problem for hypersurfaces and complete intersections. In particular, we will show that very general quartic fivefolds and complete intersections of a quadric and a cubic in $\mathrm{P}^{6}$ arestably irrational. An important new ingredient is the use of tropical degeneration techniques. These results are obtained in collaboration with Johannes Nicaise.
Keywords : rationality problem; stable rationality; toric degenerations; specialization
MSC Codes : Keywords : rationality problem; stable rationality; toric degenerations; specialization
14E05 - Rational and birational maps
14E08 - Rationality questions
14T90 - Applications of tropical geometry
Additional resources :
https://www.cirm-math.fr/RepOrga/3267/Slides/Ottem_CIRM_slides_complete.pdf
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 14/02/2025 Conference Date : 29/01/2025 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:51:03 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01-29_Ottem_2.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 1 Event 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.20294303Cite this video as: Ottem, John Christian (2025). Specialization techniques and stable rationality - Lecture 2 the motivic volume formula of Nicaise-Shinder. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20294303 URI : http://dx.doi.org/10.24350/CIRM.V.20294303 |
See Also
- [Multi angle] Resolution of foliated varieties by torus actions / Author of the conference Wlodarczyk , Jaroslaw.
- [Multi angle] Semialgebraic Whitney partition of unity / Author of the conference Valette, Anna.
- [Multi angle] Semi-homogeneous bundles, Fourier-Mukai transforms, and tropicalization / Author of the conference Ulirsch, Martin.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 3 / Author of the conference Popescu-Pampu, Patrick.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - lecture 2 / Author of the conference Popescu-Pampu, Patrick.
- [Multi angle] Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 1 / Author of the conference Popescu-Pampu, Patrick.
- [Multi angle] Specialization techniques and stable rationality - Lecture 3 / Author of the conference Ottem, John Christian.
- [Multi angle] Specialization techniques and stable rationality - Lecture 1 / Author of the conference Ottem, John Christian.
- [Multi angle] Piecewise linear geometry and spaces of valuations / Author of the conference Loeser, François.
- [Multi angle] A universal motivic invariant of birational maps / Author of the conference Lin, Hsueh-Yung.
- [Multi angle] Nash blowup fails to resolve singularities in dimensions four and higher / Author of the conference Leyton-Álvarez, Maximiliano.
- [Multi angle] A singular path through toric geometry / Author of the conference Gonzalez Perez, Pedro Daniel.
- [Multi angle] Teissier singularities / Author of the conference Mourtada, Hussein.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 3 / Author of the conference Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 2 / Author of the conference Forey, Arthur.
- [Multi angle] Motivic invariants via non-archimedean geometry - Lecture 1 / Author of the conference Forey, Arthur.
- [Multi angle] Motivic Milnor fibre and logarithmic geometry / Author of the conference Fichou, Goulwen.
- [Multi angle] Generic theta divisors / Author of the conference Budur, Nero.
- [Multi angle] The KSBA moduli space of stable log Calabi-Yau surfaces / Author of the conference Argüz, Hülya.
Bibliography
- NICAISE, Johannes et OTTEM, John Christian. Tropical degenerations and stable rationality. Duke Mathematical Journal, 2022, vol. 171, no 15, p. 3023-3075. - https://doi.org/10.1215/00127094-2022-0065
- NICAISE, Johannes et OTTEM, John Christian. A refinement of the motivic volume, and specialization of birational types. In : Rationality of varieties. Springer International Publishing, 2021. p. 291-322. - https://doi.org/10.1007/978-3-030-75421-1_11
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