Unitals in Projective Planes

This book is a monograph on unitals embedded in ?nite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are many open pr- lems, and this remains a fruitful area for Ph.D. dissertations. Unitals play an important role in ?nite geometry as well as in related areas of mathematics. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order projective plane (see Section 2.3). Moreover, unitals meet the upper bound for the number of absolute points of any polarity in a square order projective plane (see Section 1.5). From an applications point of view, the linear codes arising from unitals have excellent technical properties (see 2 Section 6.4). The automorphism group of the classical unitalH =H(2,q ) is 2-transitive on the points ofH, and so unitals are of interest in group theory. In the ?eld of algebraic geometry over ?nite ?elds,H is a maximal curve that contains the largest number of F -rational points with respect to its genus, 2 q as established by the Hasse-Weil bound.

List of contents

Preliminaries.- Hermitian Curves and Unitals.- Translation Planes.- Unitals Embedded in Desarguesian Planes.- Unitals Embedded in Non-Desarguesian Planes.- Combinatorial Questions and Associated Configurations.- Characterization Results.- Open Problems.

Summary

This book is a monograph on unitals embedded in ?nite projective planes. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order projective plane (see Section 2.3).

Product details

• Authors: Susa Barwick, Susan Barwick, Gary Ebert
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 10.10.2008
• EAN: 9780387763644
• ISBN: 978-0-387-76364-4
• No. of pages: 196
• Weight: 430 g
• Illustrations: XII, 196 p. 29 illus.
• Series: Springer Monographs in Mathematics; Schriftenreihe Markt und Marketing; Springer Monographs in Mathematics; Springer Monographs in Mathema; Schriftenreihe Markt und Marketing
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Algebra, A, geometry, Group Theory, Combinatorics, Mathematics and Statistics, Discrete Mathematics, Combinatorics & graph theory, Groups & group theory, Group Theory and Generalizations, algebra;classification;field;linear algebra;number theory