Topics on $K3$ surfaces - Lecture 3: Basic properties of $K3$ surfaces | Vidéo | Carmin.tv

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Topics on $K3$ surfaces - Lecture 3: Basic properties of $K3$ surfaces

By Alessandra Sarti

Appears in collection : Complex geometry: a modern viewpoint / Géométrie complexe : un point de vue moderne

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space. The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire. The topics of the lecture are the following:

² $K3$ surfaces in the Enriques-Kodaira classification. ² Examples; Kummer surfaces. ² Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map. ² The study of automorphisms on $K3$ surfaces: basic facts, examples. ² Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.

Information about the video

Date of recording 29/01/2019
Date of publication 07/02/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19490003
Cite this video Sarti, Alessandra (29/01/2019). Topics on $K3$ surfaces - Lecture 3: Basic properties of $K3$ surfaces. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19490003
URL https://dx.doi.org/10.24350/CIRM.V.19490003

Domain(s)

Algebraic Geometry

Bibliography

Artebani, M., Sarti, A., & Taki, S. (2011). $K3$ surfaces with non-symplectic automorphisms of prime order. With an appendix by Shigeyuki Kondo. Mathematische Zeitschrift, 268(1-2), 507-533 - https://doi.org/10.1007/s00209-010-0681-x
Barth, W.P., Hulek, K., Peters, C.A.M., & Van de Ven, A. (2004). Compact complex surfaces. (Ergebnisse der Mathematik und ihrer Grenzgebiete). Berlin: Springer - http://dx.doi.org/10.1007/978-3-642-57739-0
Beauville, A. (1996). Complex algebraic surfaces (London Mathematical Society Student Texts). Cambridge: Cambridge University Press - http://dx.doi.org/10.1017/CBO9780511623936
Garbagnati, A., & Sarti, A. (2009). Elliptic fibrations and symplectic automorphisms on $K3$ surfaces. Communications in Algebra, 37(10), 3601-3631 - https://doi.org/10.1080/00927870902828785
Garbagnati, A., & Sarti, A. (2007). Symplectic automorphisms of prime order on $K3$ surfaces. Journal of Algebra, 318(1), 323-350 - https://doi.org/10.1016/j.jalgebra.2007.04.017
Géométrie des surfaces $K3$ : modules et périodes - Séminaire Palaiseau. Astérisque, no. 126 (1985). Paris: Société Mathématique de France - http://www.numdam.org/item/AST_1985__126_/
Nikulin, V.V. (1980). Finite automorphism groups of Kähler $K3$ surfaces. Transactions of the Moscow Mathematical Society, 38, 71-135 - https://zbmath.org/?q=an%3A0454.14017
Nikulin, V.V. (1975). On Kummer surfaces. Mathematics of the USSR. Izvestiya, 9(2), 261-275 - https://doi.org/10.1070%2Fim1975v009n02abeh001477
Saint-Donat, B. (1974). Projective Models of $K3$ surfaces. American Journal of Mathematics, 96(4), 602–639 - http://dx.doi.org/10.2307/2373709

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