Français
Localization and virtual localization, with applications to quadratic curve counts and DT invariants
Multi angle
Authors : Levine, Marc (Author of the conference)
CIRM (Publisher )
14F42 - Motivic cohomology; motivic homotopy theory
14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
19E15 - Algebraic cycles and motivic cohomology (K-theory)
CIRM (Publisher )
Loading the player...
|
Abstract :
We report on the development of localization methods useful for quadratic enumerative invariants, replacing the classical Gm-action with an action by the normalizer of the diagonal torus in SL2.
We discuss applications to quadratic counts of twisted cubics in hypersurfaces and complete intersections (joint with Sabrina Pauli) as well as work by Anneloes Vierever, and our joint work with Viergever on quadratic DT invariants for Hilbert schemes of points on P3 and on (P1)3.
Keywords : localization; Bott residue formula; quadratic forms; Donaldson-Thomas invariants
MSC Codes : We discuss applications to quadratic counts of twisted cubics in hypersurfaces and complete intersections (joint with Sabrina Pauli) as well as work by Anneloes Vierever, and our joint work with Viergever on quadratic DT invariants for Hilbert schemes of points on P3 and on (P1)3.
Keywords : localization; Bott residue formula; quadratic forms; Donaldson-Thomas invariants
14F42 - Motivic cohomology; motivic homotopy theory
14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
19E15 - Algebraic cycles and motivic cohomology (K-theory)
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/11/2024 Conference Date : 04/11/2024 Subseries : Research talks arXiv category : Algebraic Topology ; Algebraic Geometry Mathematical Area(s) : Algebra ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:09:34 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-11-4_Levine.mp4 
|
Information on the Event
Event Title : Motivic homotopy in interaction / Homotopie motivique en interactionEvent Organizers : Déglise, Frédéric ; Dubouloz, Adrien ; Fasel, Jean ; Morel, Sophie ; Østvær, Paul Arne Dates : 04/11/2024 - 08/11/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3129.html
Citation Data
DOI : 10.24350/CIRM.V.20259503Cite this video as: Levine, Marc (2024). Localization and virtual localization, with applications to quadratic curve counts and DT invariants. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20259503 URI : http://dx.doi.org/10.24350/CIRM.V.20259503 |
See Also
- [Multi angle] Cellular A1-homology of smooth algebraic varieties / Author of the conference Sawant, Anand.
- [Multi angle] What motives know about periods -- and the other way around / Author of the conference Huber-Klawitter, Annette.
- [Multi angle] Quadratic enumerative invariants and local contributions / Author of the conference Pauli, Sabrina.
Bibliography
- LEVINE, Marc. Virtual Localization in equivariant Witt cohomology. arXiv preprint arXiv:2203.15887, 2022. - https://doi.org/10.48550/arXiv.2203.15887
- LEVINE, Marc. Atiyah-Bott localization in equivariant Witt cohomology. arXiv preprint arXiv:2203.13882, 2022. - https://doi.org/10.48550/arXiv.2203.13882
- LEVINE, Marc et PAULI, Sabrina. Quadratic counts of twisted cubics. arXiv preprint arXiv:2206.05729, 2022. - https://doi.org/10.48550/arXiv.2206.05729
- Perspectives on four decades of algebraic geometry Volume 2: in Memory of Alberto Collino, Progress in Mathematics volume 352 (released in 2025) -
Imagette Video
