Area in real K3-surfaces
Ilia ItenbergSorbonne Université, Paris, France
Grigory MikhalkinUniversité de Genève, Switzerland
For a real K3-surface , one can introduce areas of connected components of the real point set of using a holomorphic symplectic form of . 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 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 (where is a positive integer) and such that has one non-spherical component and at least 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 .
Cite this article
Ilia Itenberg, Grigory Mikhalkin, Area in real K3-surfaces. EMS Surv. Math. Sci. 8 (2021), no. 1/2, pp. 217–235DOI 10.4171/EMSS/48