Unitals in Projective Planes
Series: Springer Monographs in Mathematics;
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Product details:
- Edition number Softcover reprint of hardcover 1st ed. 2008
- Publisher Springer New York
- Date of Publication 6 December 2010
- Number of Volumes 1 pieces, Previously published in hardcover
- ISBN 9781441926197
- Binding Paperback
- See also 9780387763644
- No. of pages196 pages
- Size 235x155 mm
- Weight 454 g
- Language English
- Illustrations XII, 196 p. 29 illus. Illustrations, black & white 0
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Long description:
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.
MoreTable 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.
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