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Unitals in Projective Planes

  • Book
  • © 2008

Overview

Authors:
  1. Gary Ebert
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  2. Susan Barwick
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  • 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

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (8 chapters)

  1. Front Matter

    Pages 1-9
    Download chapter PDF

  2. Preliminaries

    • Susan Barwick, Gary Ebert
    Pages 1-20

  3. Hermitian Curves and Unitals

    • Susan Barwick, Gary Ebert
    Pages 1-11

  4. Translation Planes

    • Susan Barwick, Gary Ebert
    Pages 1-25

  5. Unitals Embedded in Desarguesian Planes

    • Susan Barwick, Gary Ebert
    Pages 1-29

  6. Unitals Embedded in Non-Desarguesian Planes

    • Susan Barwick, Gary Ebert
    Pages 1-20

  7. Combinatorial Questions and Associated Configurations

    • Susan Barwick, Gary Ebert
    Pages 1-23

  8. Characterization Results

    • Susan Barwick, Gary Ebert
    Pages 1-34

  9. Open Problems

    • Susan Barwick, Gary Ebert
    Pages 1-3

  10. Back Matter

    Pages 1-22
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Keywords

About this book

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.

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