Lines Tangent to 2n-2 spheres in R^n

TL;DR

This paper proves the exact number of complex common tangent lines to 2n-2 general spheres in R^n and demonstrates the existence of a configuration with all real common tangents.

Contribution

It establishes the precise count of tangent lines in complex space and shows real configurations can achieve this maximum, advancing understanding of tangent line geometry.

Findings

Number of complex common tangent lines is 3 * 2^(n-1).

Existence of sphere configurations with all real common tangents.

Results apply to general position spheres in R^n.

Abstract

We show that there are 3 \cdot 2^(n-1) complex common tangent lines to 2n-2 general spheres in R^n and that there is a choice of spheres with all common tangents real.