Unitals in Projective Planes by Susan Barwick (English) Paperback Book

Description: Unitals in Projective Planes by Susan Barwick, Gary Ebert 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). FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher 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. Notes No other book on unitals, this book will fill that voidText is clear and easy to followBook is well-structured and comprehensive with excellent diagrams Back Cover This clearly written text is the first book on unitals embedded in finite projective planes. Unitals are key structures in square order projective planes, and have connections with other structures in algebra. They provide a link between groups and geometries. There is a considerable number of research articles concerning unitals, and there also exist many open problems. This book is a thorough survey of the research literature on embedded unitals which collects this material in book form for the first time. The book is aimed at graduate students and researchers who want to learn about this topic without reading all the original articles. The primary proof techniques used involve linear algebraic arguments, finite field arithmetic, some elementary number theory, and combinatorial enumeration. Some computer results not previously found in the literature also are mentioned in the text. The authors have included a comprehensive bibliography which will become an invaluable resource. Gary Ebert is Professor of Mathematics at the University of Delaware, USA. Susan Barwick is a Senior Lecturer of Mathematics at the University of Adelaide, Australia. Table 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. 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. Feature No other book on unitals, this book will fill that void Text is clear and easy to follow Book is well-structured and comprehensive with excellent diagrams Details ISBN1441926194 Author Gary Ebert Publisher Springer-Verlag New York Inc. Series Springer Monographs in Mathematics Year 2010 Edition 1st ISBN-10 1441926194 ISBN-13 9781441926197 Format Paperback Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 510 Short Title UNITALS IN PROJECTIVE PLANES Language English Media Book Pages 196 Publication Date 2010-12-06 AU Release Date 2010-12-06 NZ Release Date 2010-12-06 US Release Date 2010-12-06 UK Release Date 2010-12-06 Edition Description Softcover reprint of hardcover 1st ed. 2008 Alternative 9780387763644 Audience Professional & Vocational Illustrations 29 Illustrations, black and white; XII, 196 p. 29 illus. We've got this At The Nile, if you're looking for it, we've got it. 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