Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 2, pp. 301-309 (2005)

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Conic sections in space defined by intersection conditions

Hans-Peter Schröcker

Institute of Discrete Mathematics and Geometry, Technical University Vienna

Abstract: We investigate and visualize the set of planes in complex projective three-space ${\mathbb P}^3$ that intersect $m$ conics $C_i$ and $n=6-2m$ straight lines $L_j$ in a total of six points of a conic. The solution manifold $\{mathcal S}_m$ is algebraic and of class $8-m$. It contains the pencils of planes through $L_j$ with multiplicity two and the planes of the conics $C_i$ with multiplicity three.

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Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.

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