Area in real K3-surfaces

Abstract

For a real K3-surface $X$, one can introduce areas of connected components of the real point set $\mathbb{R}X$ of $X$ using a holomorphic symplectic form of $X$. These areas are defined up to simultaneous multiplication by a positive real number, so the areas of different components can be compared. In particular, it turns out that the area of a non-spherical component of $\mathbb{R}X$ is always greater than the area of any spherical component.