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H 1 Curve neighbourhoods for odd symplectic Grassmannians

Auteurs : Pech, Clélia (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Odd symplectic Grassmannians are a family of quasi-homogeneous varieties with properties nevertheless similar to those of homogeneous spaces, such as the existence of a Schubert-type cohomology basis. In this talk based on joint work with Ryan Shifler, I will explain how to construct their curve neighbourhoods. Curve neighbourhoods were first introduced by Buch, Chaput, Mihalcea and Perrin in the homogeneous setting: it is the union of all rational curves of fixed degree passing through a given Schubert variety. Potential applications include the computation of minimal degrees in quantum cohomology.

    Keywords : odd symplectic Grassmannians; curve neighbourhoods; quantum cohomology

    Codes MSC :
    14M15 - Grassmannians, Schubert varieties, flag manifolds
    14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
    14N15 - Classical problems, Schubert calculus


    Ressources complémentaires :
    https://www.cirm-math.fr/RepOrga/2221/Slides/Pech-slides.pdf


      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 11/01/2021
      Date de captation : 18/12/2020
      Collection : Research talks ; Combinatorics ; Algebraic and Complex Geometry
      Durée : 00:55:44
      Domaine : Combinatorics ; Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-12-18_Pech.mp4

    Informations sur la Rencontre Virtuelle

    Nom de la rencontre : Quantum Groups and Cohomology Theory of Quiver and Flag Varieties / Groupes quantiques et théories cohomologiques des variétés de drapeaux et variétés carquois
    Organisateurs de la rencontre : Leclerc, Bernard ; Mihalcea, Leonardo ; Perrin, Nicolas ; Varagnolo, Michela
    Dates : 14/12/2020 - 18/12/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2221.html

    Citation Data

    DOI : 10.24350/CIRM.V.19693603
    Cite this video as: Pech, Clélia (2020). Curve neighbourhoods for odd symplectic Grassmannians.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19693603
    URI : http://dx.doi.org/10.24350/CIRM.V.19693603


    Voir aussi

    Bibliographie

    1. BUCH, Anders S., CHAPUT, Pierre-Emmanuel, MIHALCEA, Leonardo C., et al. Finiteness of cominuscule quantum $ K $-theory. In : Annales scientifiques de l'École Normale Supérieure. 2013. p. 477-494. - https://doi.org/10.24033/asens.2194

    2. BUCH, Anders S., MIHALCEA, Leonardo C., et al. Curve neighborhoods of Schubert varieties. Journal of Differential Geometry, 2015, vol. 99, no 2, p. 255-283. - https://doi.org/10.4310/jdg/1421415563

    3. GONZALES, Richard, PECH, Clélia, PERRIN, Nicolas, et al. Geometry of horospherical varieties of Picard rank one. arXiv preprint arXiv:1803.05063, 2018. - https://arxiv.org/abs/1803.05063

    4. LI, Changzheng, MIHALCEA, Leonardo C., et SHIFLER, Ryan M. Conjecture O holds for the odd symplectic Grassmannian. Bulletin of the London Mathematical Society, 2019, vol. 51, no 4, p. 705-714. - https://doi.org/10.1112/blms.12268

    5. MIHAI, Ion Alexandru. Odd symplectic flag manifolds. Transformation groups, 2007, vol. 12, no 3, p. 573-599. - http://dx.doi.org/10.1007/s00031-006-0053-0

    6. MIHALCEA, Leonardo C. et SHIFLER, Ryan M. Equivariant quantum cohomology of the odd symplectic Grassmannian. Mathematische Zeitschrift, 2019, vol. 291, no 3-4, p. 1569-1603. - https://doi.org/10.1007/s00209-018-2120-3

    7. PASQUIER, Boris. On some smooth projective two-orbit varieties with Picard number 1. Mathematische Annalen, 2009, vol. 344, no 4, p. 963-987. - http://dx.doi.org/10.1007/s00208-009-0341-9

    8. PECH, Clélia. Quantum cohomology of the odd symplectic Grassmannian of lines. Journal of Algebra, 2013, vol. 375, p. 188-215. - https://doi.org/10.1016/j.jalgebra.2012.11.010

    9. PROCTOR, Robert A. Odd symplectic groups. Inventiones mathematicae, 1988, vol. 92, no 2, p. 307-332. - https://doi.org/10.1007/BF01404455

    10. SHIFLER, Ryan M. et WITHROW, Camron. Minimum Quantum Degrees for Isotropic Grassmannians in Types B and C. arXiv preprint arXiv:2004.00084, 2020. - https://arxiv.org/abs/2004.00084

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