Area in real K3-surfaces

  • Ilia Itenberg

    Sorbonne Université, Paris, France
  • Grigory Mikhalkin

    Université de Genève, Switzerland
Area in real K3-surfaces cover
Download PDF

This article is published open access under our Subscribe to Open model.


For a real K3-surface XX, one can introduce areas of connected components of the real point set RX\mathbb{R}X of XX using a holomorphic symplectic form of XX. 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 RX\mathbb{R}X is always greater than the area of any spherical component.

In this paper we explore further comparative restrictions on the area for real K3-surfaces admitting a suitable polarization of degree 2g22g - 2 (where gg is a positive integer) and such that RX\mathbb{R}X has one non-spherical component and at least gg spherical components. For this purpose we introduce and study the notion of simple Harnack curves in real K3-surfaces, generalizing planar simple Harnack curves from [8].

Cite this article

Ilia Itenberg, Grigory Mikhalkin, Area in real K3-surfaces. EMS Surv. Math. Sci. 8 (2021), no. 1/2, pp. 217–235

DOI 10.4171/EMSS/48