Real split hyperplane sections on smooth polarized $K3$-surfaces

TL;DR

This paper establishes upper bounds, often sharp, on the number of real hyperplane sections of real smooth polarized K3-surfaces that decompose into lines, aligning with complex case bounds in most instances.

Contribution

It provides new sharp upper bounds for real hyperplane sections on polarized K3-surfaces, extending understanding of their geometric properties.

Findings

Most bounds match complex case bounds

Bounds are sharp in most cases

Provides new insights into real hyperplane sections

Abstract

We find upper bounds, sharp in most cases, on the number of real hyperplane sections of real smooth polarized $K3$-surfaces that split into lines. Most bounds coincide with their complex counterparts.