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Localization and virtual localization, with applications to quadratic curve counts and DT invariants

Apparaît dans la collection : Motivic homotopy in interaction / Homotopie motivique en interaction

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.

Informations sur la vidéo

Date de captation 04/11/2024
Date de publication 18/11/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20259503
Citer cette vidéo Levine, Marc (04/11/2024). Localization and virtual localization, with applications to quadratic curve counts and DT invariants. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20259503
URL https://dx.doi.org/10.24350/CIRM.V.20259503

Domaine(s)

Bibliographie

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) -

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