Curve neighbourhoods for odd symplectic Grassmannians | Vidéo | Carmin.tv

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Curve neighbourhoods for odd symplectic Grassmannians

By Clélia Pech

Appears in collection : Quantum Groups and Cohomology Theory of Quiver and Flag Varieties / Groupes quantiques et théories cohomologiques des variétés de drapeaux et variétés carquois

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.

Information about the video

Date of recording 18/12/2020
Date of publication 11/01/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19693603
Cite this video Pech, Clélia (18/12/2020). Curve neighbourhoods for odd symplectic Grassmannians. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19693603
URL https://dx.doi.org/10.24350/CIRM.V.19693603

Domain(s)

Bibliography

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

MSC codes

Document(s)

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

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