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Automorphisms of hyperkähler manifolds - Lecture 1
Post-edited
Authors : Sarti, Alessandra (Author of the conference)
CIRM (Publisher )
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 (Publisher )
Abstract :
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).
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 14/12/2017 Conference Date : 11/12/2017 Subseries : Research talks arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:49:33 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-12-11_Sarti_Part1.mp4 
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Information on the Event
Event Title : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexeEvent Organizers : Broustet, Amaël ; Pasquier, Boris Dates : 11/12/2017 - 15/12/2017 Event Year : 2017 Event URL : https://conferences.cirm-math.fr/1692.html
Citation Data
DOI : 10.24350/CIRM.V.19256903Cite this video as: 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 |
See Also
- [Multi angle] Group actions on quiver moduli spaces and applications / Author of the conference Hoskins, Victoria.
- [Multi angle] Orbital degeneracy loci / Author of the conference Benedetti, Vladimiro.
- [Multi angle] Automorphisms of hyperkähler manifolds - Lecture 3 / Author of the conference Sarti, Alessandra.
- [Multi angle] Automorphisms of hyperkähler manifolds - Lecture 2 / Author of the conference Sarti, Alessandra.
Bibliography
- 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
