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Transactions of the American Mathematical Society

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Lines tangent to $2n-2$ spheres in ${\mathbb R}^n$

Authors: Frank Sottile and Thorsten Theobald
Journal: Trans. Amer. Math. Soc. 354 (2002), 4815-4829
MSC (2000): Primary 14N10, 14P99, 51N20, 52A15, 68U05
Published electronically: June 5, 2002
MathSciNet review: 1926838
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Abstract: We show that for $n \ge 3$there are $3 \cdot 2^{n-1}$ complex common tangent lines to $2n-2$ general spheres in $\mathbb{R}^n$ and that there is a choice of spheres with all common tangents real.

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Additional Information

Frank Sottile
Affiliation: Department of Mathematics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, Massachusetts 01003

Thorsten Theobald
Affiliation: Zentrum Mathematik, Technische Universität München, München, Germany

Received by editor(s): June 10, 2001
Received by editor(s) in revised form: October 29, 2001
Published electronically: June 5, 2002
Additional Notes: Research of first author supported in part by NSF grant DMS-0070494
Article copyright: © Copyright 2002 American Mathematical Society

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