2007 | Book
q-Clan Geometries in Characteristic 2
Book Series: Frontiers in Mathematics
Authors: Ilaria Cardinali, Stanley E. Payne
Publisher: Birkhäuser Basel
Print ISBN: 978-3-7643-8507-1
Electronic ISBN: 978-3-7643-8508-8
2007 | Book
Book Series: Frontiers in Mathematics
Authors: Ilaria Cardinali, Stanley E. Payne
Publisher: Birkhäuser Basel
Print ISBN: 978-3-7643-8507-1
Electronic ISBN: 978-3-7643-8508-8
A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely.