On tangents to quadric surfaces

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We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to configurations of four quadrics admitting a continuum of common tangents. We formulate geometrical conditions in the projective space defined by all complex quadric surfaces which express the fact that several quadrics are tangent along a curve to one and the same quadric of rank at least three, and called, for intuitive reasons: a basket. Lines in any ruling of the latter will be common tangents. These considerations are then restricted to spheres in Euclidean three-space, and result in a complete answer to the question over the reals: ``When do four spheres allow infinitely many common tangents?''.
50 pages

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Algebraic Geometry, 14N05 (Primary) 14J28, 14P05 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/70263

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0402394
 http://arxiv.org/abs/math/0402394

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arXiv