English
Curve neighbourhoods for odd symplectic Grassmannians
Virtualconference
Auteurs : Pech, Clélia (Auteur de la conférence)
CIRM (Editeur )
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
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.
Mots-Clés : odd symplectic Grassmannians; curve neighbourhoods; quantum cohomology
Codes MSC : Mots-Clés : odd symplectic Grassmannians; curve neighbourhoods; quantum cohomology
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 11/01/2021 Date de Captation : 18/12/2020 Sous Collection : Research talks Catégorie arXiv : Algebraic Geometry ; Combinatorics Domaine(s) : Combinatoires ; Géométrie Complexe & géométrie Algébrique Format : MP4 (.mp4) - HD Durée : 00:55:44 Audience : Chercheurs Download : https://videos.cirm-math.fr/2020-12-18_Pech.mp4 
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Informations sur la Rencontre
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 carquoisOrganisateurs de la Rencontre : Leclerc, Bernard ; Mihalcea, Leonardo ; Perrin, Nicolas ; Varagnolo, Michela Dates : 14/12/2020 - 18/12/2020 Année de la rencontre : 2020 URL de la Rencontre : https://conferences.cirm-math.fr/2221.html
Données de citation
DOI : 10.24350/CIRM.V.19693603Citer cette vidéo: 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 |
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Bibliographie
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- PROCTOR, Robert A. Odd symplectic groups. Inventiones mathematicae, 1988, vol. 92, no 2, p. 307-332. - https://doi.org/10.1007/BF01404455
- 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
