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Topics on $K3$ surfaces - Lecture 5: Finite automorphism groups
Multi angle
Authors : Sarti, Alessandra (Author of the conference)
CIRM (Publisher )
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)
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 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.
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)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 07/02/2019 Conference Date : 29/01/2019 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:01:57 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2019-01-29_Sarti_5.mp4 
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Information on the Event
Event Title : Complex geometry: a modern viewpoint / Géométrie complexe : un point de vue moderneEvent Organizers : Keller, Julien ; Roulleau, Xavier ; Rousseau, Erwan Dates : 28/01/2019 - 01/02/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2098.html
Citation Data
DOI : 10.24350/CIRM.V.19490203Cite this video as: Sarti, Alessandra (2019). Topics on $K3$ surfaces - Lecture 5: Finite automorphism groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19490203 URI : http://dx.doi.org/10.24350/CIRM.V.19490203 |
See Also
- [Multi angle] Topics on $K3$ surfaces - Lecture 6: Classification / Author of the conference Sarti, Alessandra.
- [Multi angle] Topics on $K3$ surfaces - Lecture 4: Nèron-Severi group and automorphisms / Author of the conference Sarti, Alessandra.
- [Multi angle] Topics on $K3$ surfaces - Lecture 3: Basic properties of $K3$ surfaces / Author of the conference Sarti, Alessandra.
- [Multi angle] Topics on $K3$ surfaces - Lecture 2: Kummer surfaces / Author of the conference Sarti, Alessandra.
- [Post-edited] Topics on $K3$ surfaces - Lecture 1: $K3$ surfaces in the Enriques Kodaira classification and examples / Author of the conference Sarti, Alessandra.
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
