Geodesic
On the connected components of moduli of real polarized K3-surfaces
Izvestiya. Mathematics , Tome 72 (2008) no. 1, pp. 91-111

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We complete the investigations in [11] on the classification of connected components of moduli of real polarized K3-surfaces. In particular, we show that this classification is closely related to some classical problems in number theory: the classification of binary indefinite lattices and the representation of integers as sums of two squares. As an application, we use recent results in [13] to completely classify real polarized K3-surfaces that are deformations of real hyperelliptically polarized K3-surfaces. This is important because real hyperelliptically polarized K3-surfaces can be constructed explicitly.
Keywords: deformation, real $K3$ surface, connected component, hyperelliptic curve, linear system, real rational surface, ellipsoid, hyperboloid, polarization.
Mots-clés : moduli 
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V. V. Nikulin. On the connected components of moduli of real polarized K3-surfaces. Izvestiya. Mathematics , Tome 72 (2008) no. 1, pp. 91-111. http://geodesic.mathdoc.fr/item/IM2_2008_72_1_a4/