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Real K3 surfaces with non-symplectic involution and applications

2005; Wiley; Volume: 90; Issue: 03 Linguagem: Inglês

10.1112/s0024611505015212

1460-244X

Viacheslav V. Nikulin, Sachiko Saito,

Geometric and Algebraic Topology

Proceedings of the London Mathematical SocietyVolume 90, Issue 3 p. 591-654 Articles Real K3 Surfaces with Non-Symplectic Involution and Applications Viacheslav V. Nikulin, Viacheslav V. Nikulin [email protected] Department of Pure Mathematics, The University of Liverpool, Liverpool, L69 3BX United KingdomSearch for more papers by this authorSachiko Saito, Sachiko Saito [email protected] Department of Mathematics Education, Hakodate Campus, Hokkaido University of Education, Hakodate, 040-8567 JapanSearch for more papers by this author Viacheslav V. Nikulin, Viacheslav V. Nikulin [email protected] Department of Pure Mathematics, The University of Liverpool, Liverpool, L69 3BX United KingdomSearch for more papers by this authorSachiko Saito, Sachiko Saito [email protected] Department of Mathematics Education, Hakodate Campus, Hokkaido University of Education, Hakodate, 040-8567 JapanSearch for more papers by this author First published: 23 December 2016 https://doi.org/10.1112/S0024611505015212Citations: 11AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract Classification of real K3 surfaces X with non-symplectic involution τ is considered. We define a natural notion of degeneration for them. We show that the connected component of moduli of non-degenerate surfaces of this type is defined by the isomorphism class of the action of τ and the anti-holomorphic involution φ in the homology lattice. (There are very few similar results known.) For their classification we apply invariants of integral lattice involutions with conditions that were developed by the first author in 1983. As a particular case, we describe connected components of moduli of real non-singular curves A ∈ ∣−2KV∣ for the classical real surfaces: V = P2, hyperboloid, ellipsoid, F1, F4. As an application, we describe all real polarized K3 surfaces that are deformations of general real K3 double rational scrolls (the surfaces V above). There are very few exceptions. For example, any non-singular real quartic in P3 can be constructed in this way. 2000 Mathematics Subject Classification 14H45, 14J26, 14J28, 14P25. Citing Literature Volume90, Issue3May 2005Pages 591-654 RelatedInformation