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

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.Comment: Minor revisions. Trans. AMer. Math. Soc., to appear. 15 pages, 3 .eps figures; also a web page with computer code verifying the computations in the paper and with additional picture