论文标题
真正的K3曲面区域
Area in real K3-surfaces
论文作者
论文摘要
对于真实的K3-Surface $ x $，可以使用$ x $的Holomorphic Sympletic形式介绍真实点集合$ \ MATHBB {r} x $ $ x $的连接组件的区域。这些区域定义为同时乘以乘以正实数，因此可以比较不同组件的区域。特别是，事实证明，$ \ mathbb {r} x $的非球形组件的面积总是大于任何球形组件的区域。 在本文中，我们探讨了对真正的K3曲面区域的进一步比较限制，以承认合适的度量$ 2G-2 $（其中$ g $是一个正整数），因此，$ \ mathbb {r} x $具有一个非球形组件和至少$ g $ g $球形组件。为此，我们介绍并研究了真正的K3曲面中简单harnack曲线的概念，从而概括了平面简单的harnack曲线。
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. In this paper we explore further comparative restrictions on the area for real K3-surfaces admitting a suitable polarization of degree $2g - 2$ (where $g$ is a positive integer) and such that $\mathbb{R} X$ has one non-spherical component and at least $g$ spherical components. For this purpose we introduce and study the notion of simple Harnack curves in real K3-surfaces, generalizing planar simple Harnack curves.
