Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 2, pp. 527-541 (2006)

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The Betten-Walker Spread and Cayley's Ruled Cubic Surface

Hans Havlicek and Rolf Riesinger

Institut f{ü}r Diskrete Mathematik und Geometrie, Technische Universit{ä}t Wien, Wiedner Hauptstra{ß}e 8--10/104, A-1040 Wien, Austria, e-mail:; Patrizigasse 7/14, A-1210 Wien, Austria, e-mail:

Abstract: We establish that, over certain ground fields, the set of osculating tangents of Cayley's ruled cubic surface gives rise to a (maximal partial) spread which is also a dual (maximal partial) spread. It is precisely the Betten-Walker spreads that allow for this construction. Every infinite Betten-Walker spread is not an algebraic set of lines, but it turns into such a set by adding just one pencil of lines.

Keywords: Cayley's ruled cubic surface, osculating tangents, maximal partial spread, maximal partial dual spread, algebraic set of lines

Classification (MSC2000): 51A40, 51M30, 14J26

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Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.

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