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Real K3 surfaces with non‐symplectic involution and applications. II
Author(s) -
Nikulin Viacheslav V.,
Saito Sachiko
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl023
Subject(s) - mathematics , symplectic geometry , elliptical polarization , moduli , moduli space , pure mathematics , quadratic equation , mathematical analysis , geometry , physics , optics , quantum mechanics , linear polarization , laser
We consider real forms of rational surfaces F m with Picard number 2. Connected components of moduli of real non‐singular curves in | − 2F m | have been classified recently by us for m = 0, 1, 4. Applying similar methods, here we fill the gap for m = 2 and m = 3 to complete a similar classification for any 0 ⩽ m ⩽ 4, when | − 2F m | is reduced. The case of F 2 is especially remarkable and classical (the quadratic cone in ℙ 3 ). As an application, we complete the classification of connected components of moduli of real hyper‐elliptically polarized K3 surfaces and the classification of deformations of real hyper‐elliptically polarized K3 surfaces to real polarized K3 surfaces started by us in 2005. This could be important in some questions because real hyper‐elliptically polarized K3 surfaces can be constructed explicitly.