https://cdn.jwplayer.com/libraries/kxatZa2V.js CIRM - Videos & books Library - Automorphisms of hyperkähler manifolds​ - Lecture 1
En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK
2

Automorphisms of hyperkähler manifolds​ - Lecture 1

Bookmarks Report an error
Post-edited
Authors : Sarti, Alessandra (Author of the conference)
CIRM (Publisher )

Loading the player...
irreducible holomorphic symplectic manifolds examples of irreducible holomorphic symplectic manifolds properties of Hilbert schemes lattice properties of irreducible holomorphic symplectic manifolds automorphisms of irreducible holomorphic symplectic manifolds properties of automorphisms questions of the audience

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

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : 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

Information on the Event

Event Title : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexe
Event 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.19256903
Cite 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

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



Bookmarks Report an error