Nikulin; real polarized K3 surfaces, 2008 | K3 surfaces with involutions
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K3 surfaces with involutions

Local and global Torelli theorems for complex K3 surfaces, periods of K3 surfaces, non-symplectic holomorphic involutions, anti-holomorphic involutions, Hilbert schemes of K3 surfaces, Nikulin's lattice theory, lattice-polarized K3 surfaces. . .

Nikulin; real polarized K3 surfaces, 2008

V.V. Nikulin;

On the connected components of moduli of real polarized K3 surfaces

Izvestiya: Mathematics 72:1 (2008), 91--111.

Abstract.

We complete the investigations in [11] on the classification of connected components of moduli of real polarized $ \mathrm 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 $ \mathrm K3$-surfaces that are

deformations of real hyperelliptically polarized $ \mathrm K3$-surfaces.

This is important because

real hyperelliptically polarized $ \mathrm K3$-surfaces

can be constructed explicitly.

 

Mathematics Subject Classification: 14H45, 14J26, 14J28, 14P25

[11] Nikulin; Integral ・・・・　(1979).

[13] Nikulin and Saito; Real K3・・・・　Proc LMS 90 (2005)