The Betten-Walker spread and Cayley's ruled cubic surface

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. 2000 Mathematics Subject Classification. 51A40, 51M30, 14J26.