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Regular Hyperbolic Fibrations by R. D. Baker; G. L. Ebert; K. L. Wantz is a Mathematics article available to read on EtoBox.
What is Regular Hyperbolic Fibrations about?
A hyperbolic ®bration is a set of q À 1 hyperbolic quadrics and two lines which together partition the points of PG3Y q. The classical example of a hyperbolic ®bration comes from a pencil of quadrics; however, several other families are now known. In this paper we begin the development of a general framework to study hyperbolic ®brations for odd prime powers q. One byproduct of hyperbolic ®brations is the 2 qÀ1 (not necessarily inequivalent) spreads of PG3Y q they spawn via the selection of one ruling family of lines for each of the hyperbolic quadrics. We show how the hyperbolic ®bration context can be used to unify the study of these spreads, especially those associated with j-planes. The question of whether a spread spawned from such a ®bration could contain any reguli other than the ones it inherits from the ®bration plays a signi®cant role in the determination of its automorphism group, as well as being an interesting geometric question in its own right. This information is then used to address the problem of sorting out projective equivalences among the spreads spawned from a given hyperbolic ®bration. Plu È cker coordinates are an important tool in most of these investigatio
Who reads Regular Hyperbolic Fibrations?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- R. D. Baker; G. L. Ebert; K. L. Wantz
- Publisher
- Walter de Gruyter GmbH
- Published
- 2001
- Language
- EN
- Field
- Mathematics (Physical Sciences)