Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 527541 (2006) 

The BettenWalker Spread and Cayley's Ruled Cubic SurfaceHans Havlicek and Rolf RiesingerInstitut f{ü}r Diskrete Mathematik und Geometrie, Technische Universit{ä}t Wien, Wiedner Hauptstra{ß}e 810/104, A1040 Wien, Austria, email: havlicek@geometrie.tuwien.ac.at; Patrizigasse 7/14, A1210 Wien, Austria, email: rolf.riesinger@chello.atAbstract: 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 BettenWalker spreads that allow for this construction. Every infinite BettenWalker 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 Full text of the article:
Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.
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