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H 1 Automorphisms of hyperkähler manifolds​ - Lecture 2

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

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    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 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.19257203
    Cite this video as: Sarti, Alessandra (2017). Automorphisms of hyperkähler manifolds​ - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19257203
    URI : http://dx.doi.org/10.24350/CIRM.V.19257203


    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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