English
Automorphisms of hyperkähler manifolds - Lecture 1
Post-edited
Auteurs : Sarti, Alessandra (Auteur de la Conférence)
CIRM (Editeur )
14J28 - $K3$ surfaces and Enriques surfaces
14J35 - Algebraic $4$-folds
14J50 - Automorphisms of surfaces and higher-dimensional varieties
14J70 - Algebraic hypersurfaces
14M15 - Grassmannians, Schubert varieties, flag manifolds
14N20 - Configurations and arrangements of linear subspaces
CIRM (Editeur )
Résumé :
In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and describe some explicit examples. I will give particular attention to double EPW sextics, that admit in a natural way a non-symplectic involution. Time permitting I will show how the rich geometry of double EPW sextics has an important connection to a classical question of U. Morin (1930).
Codes MSC : 14J28 - $K3$ surfaces and Enriques surfaces
14J35 - Algebraic $4$-folds
14J50 - Automorphisms of surfaces and higher-dimensional varieties
14J70 - Algebraic hypersurfaces
14M15 - Grassmannians, Schubert varieties, flag manifolds
14N20 - Configurations and arrangements of linear subspaces
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 14/12/2017 Date de captation : 11/12/2017 Sous collection : Research talks arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 00:49:33 Audience : Researchers Download : https://videos.cirm-math.fr/2017-12-11_Sarti_Part1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexeOrganisateurs de la rencontre : Broustet, Amaël ; Pasquier, Boris Dates : 11/12/2017 - 15/12/2017 Année de la rencontre : 2017 URL Congrès : https://conferences.cirm-math.fr/1692.html
Données de citation
DOI : 10.24350/CIRM.V.19256903Citer cette vidéo: Sarti, Alessandra (2017). Automorphisms of hyperkähler manifolds - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19256903 URI : http://dx.doi.org/10.24350/CIRM.V.19256903 |
Voir aussi
- [Multi angle] Group actions on quiver moduli spaces and applications / Auteur de la Conférence Hoskins, Victoria.
- [Multi angle] Orbital degeneracy loci / Auteur de la Conférence Benedetti, Vladimiro.
- [Multi angle] Automorphisms of hyperkähler manifolds - Lecture 3 / Auteur de la Conférence Sarti, Alessandra.
- [Multi angle] Automorphisms of hyperkähler manifolds - Lecture 2 / Auteur de la Conférence Sarti, Alessandra.
Bibliographie
- Boissière, S., Camere, C., & Sarti, A. (2016). Classification of automorphisms on a deformation family of hyper-Kähler four-folds by $p$-elementary lattices. Kyoto Journal of Mathematics, 56(3), 465-499 - https://doi.org/10.1215/21562261-3600139
- Boissière, S., Cattaneo, A., Nieper-Wisskirchen, M., & Sarti, A. (2016). The automorphism group of the Hilbert scheme of two points on a generic projective $K3$ surface. In C. Faber, G. Farkas, & G. van der Geer (Eds.), $K3$ surfaces and their moduli (pp. 1-15). Cham: Birkhäuser - https://doi.org/10.1007/978-3-319-29959-4_1
- Donten-Bury, M., van Geemen, B., Kapustka, G., Kapustka, M., & Wisniewski, J.A. (2017). A very special EPW sextic and two IHS fourfolds. Geometry & Topology, 21 (2), 1179-1230 - https://doi.org/10.2140/gt.2017.21.1179
- O'Grady, K.G. (2013). Pairwise incident planes and hyperkähler four-folds. In B. Hassett, J. McKernan, J. Starr, & R. Vakil (Eds.), A celebration of algebraic geometry (pp. 553-566). Providence, RI: American Mathematical Society; Cambridge, MA: Clay Mathematics Institute - http://www.arxiv.org/abs/1204.6257
