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H 2 Automorphisms of hyperkähler manifolds​ - Lecture 1

Auteurs : Sarti, Alessandra (Auteur de la Conférence)
CIRM (Editeur )

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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

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

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 14/12/2017
    Date de captation : 11/12/2017
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:49:33
    Domaine : Algebraic & Complex Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2017-12-11_Sarti_Part1.mp4

Informations sur la rencontre

Nom du congrès : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexe
Organisteurs Congrès : 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

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

Voir aussi

Bibliographie

  1. 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

  2. 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

  3. 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

  4. 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



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