CIRM - Videos & books Library - Topics on $K3$ surfaces - Lecture 1: $K3$ surfaces in the Enriques Kodaira classification and examples

Post-edited

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

Loading the player...

Enriques-Kodaira classification Kodaira dimension quartics complete intersections double plane

Résumé : 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:

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

Codes MSC :
14C20 - Divisors, linear systems, invertible sheaves
14C22 - Picard groups
14J10 - Families, moduli, classification: algebraic theory
14J27 - Elliptic surfaces
14J28 - $K3$ surfaces and Enriques surfaces
14J50 - Automorphisms of surfaces and higher-dimensional varieties
14L30 - Group actions on varieties or schemes (quotients)

Informations sur la Vidéo

Langue :

Date de publication :

Date de captation :

Sous collection :

arXiv category :

Domaine :

Format :

Durée :

Audience :

Download :

https://videos.cirm-math.fr/2019-01-28-Sarti_1.mp4

Informations sur la Rencontre

Nom de la rencontre : Complex geometry: a modern viewpoint / Géométrie complexe : un point de vue moderne
Organisateurs de la rencontre : Keller, Julien ; Roulleau, Xavier ; Rousseau, Erwan
Dates : 28/01/2019 - 01/02/2019
Année de la rencontre : 2019
URL Congrès : https://conferences.cirm-math.fr/2098.html

Données de citation

DOI : 10.24350/CIRM.V.19489603
Citer cette vidéo: Sarti, Alessandra (2019). Topics on $K3$ surfaces - Lecture 1: $K3$ surfaces in the Enriques Kodaira classification and examples. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19489603
URI : http://dx.doi.org/10.24350/CIRM.V.19489603

Bibliographie

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

ASarti1.jpg