Real K3 surfaces with non-symplectic involution and applications. II

Details Real K3 surfaces with non-symplectic involution and applications. II Real K3 surfaces with non-symplectic involution and applications. II

2005-08-24

arxiv.org/abs/math/0508478v1

Proc. Lond. Math. Soc. (3) 95 (2007), no. 1, 20-48

Mathematics

Algebraic Geometry

22 pages, 6 figures

Scientific paper

We consider real forms of relatively minimal rational surfaces F_m. Connected components of moduli of real non-singular curves in |-2K_{F_m}| had been classified recently for m=0, 1, 4 in math.AG/0312396. Applying similar methods, here we fill the gap for m=2 and m=3 to complete similar classification for any 0\le m\le 4 when |-2K_{F_m}| is reduced. The case of F_2 is especially remarkable and classical (quadratic cone in P^3). As an application, we finished classification of connected components of moduli of real hyper-elliptically polarized K3 surfaces and their deformations to real polarized K3 surfaces started in math.AG/0312396, math.AG/0507197. This could be important in some questions because real hyper-elliptically polarized K3 surfaces can be constructed explicitly.

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