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The Resource Unitals in projective planes, Susan Barwick, Gary Ebert

Unitals in projective planes, Susan Barwick, Gary Ebert

Label
Unitals in projective planes
Title
Unitals in projective planes
Statement of responsibility
Susan Barwick, Gary Ebert
Creator
Contributor
Subject
Language
eng
Member of
Cataloging source
YDXCP
http://library.link/vocab/creatorName
Barwick, Susan
Dewey number
516.5
Illustrations
illustrations
Index
index present
LC call number
QA471
LC item number
.B37 2008
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Ebert, Gary
Series statement
Springer monographs in mathematics
http://library.link/vocab/subjectName
Projective planes
Label
Unitals in projective planes, Susan Barwick, Gary Ebert
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 9
  • 117
  • 6.3
  • Related Combinatorial Structures
  • 121
  • 6.3.1
  • Inversive Planes
  • 121
  • 6.3.2
  • Arcs
  • 123
  • 1.4
  • 6.4
  • Unitals and Codes
  • 127
  • 7
  • Characterization Results
  • 133
  • 7.1
  • Characterizations of Unitals via Baer Sublines
  • 133
  • 7.2
  • Ovals and Ovoids
  • Proofs of Results from Section 7.1
  • 136
  • 7.3
  • Other Configurational Characterizations
  • 148
  • 7.3.1
  • Tallini Scafati Characterizations
  • 148
  • 7.3.2
  • Characterizations Using Feet
  • 12
  • 153
  • 7.3.3
  • Characterizations Using O'Nan Configurations
  • 161
  • 7.4
  • Characterizations Using the Quadratic Extension PG(4, q[superscript 2])
  • 164
  • 7.5
  • The Bose Representation of PG(2, q[superscript 2]) in PG(5, q)
  • 164
  • 1.5
  • 7.6
  • Group Theoretic Characterizations
  • 166
  • 8
  • Open Problems
  • 167
  • A Nomenclature of Unitals
  • 171
  • B
  • Group Theoretic Characterizations of Unitals
  • Some Linear Algebra
  • 173
  • 13
  • 2
  • Hermitian Curves and Unitals
  • 21
  • 1.1
  • 2.1
  • Nondegenerate Hermitian Curves
  • 21
  • 2.2
  • Degenerate Hermitian Curves and Baer Sublines
  • 24
  • 2.3
  • Unitals
  • 27
  • 3
  • Affine and Projective Geometries
  • Translation Planes
  • 33
  • 3.1
  • Translation Planes
  • 33
  • 3.2
  • Derivation
  • 34
  • 3.3
  • Spreads
  • 1
  • 36
  • 3.4
  • The Bruck-Bose Representation
  • 41
  • 3.4.1
  • The Bruck-Bose Construction
  • 41
  • 3.4.2
  • Baer Subplanes and Baer Sublines in Bruck-Bose
  • 43
  • 1.2
  • 3.4.3
  • Derivation in Bruck-Bose
  • 52
  • 3.4.4
  • Coordinates in Bruck-Bose
  • 53
  • 4
  • Unitals Embedded in Desarguesian Planes
  • 59
  • 4.1
  • Finite Fields
  • Buekenhout Constructions
  • 59
  • 4.2
  • Unitals Embedded in PG(2, q[superscript 2])
  • 66
  • 4.2.1
  • The Odd Characteristic Case
  • 66
  • 4.2.2
  • The Even Characteristic Case
  • 8
  • 79
  • 5
  • Unitals Embedded in Non-Desarguesian Planes
  • 89
  • 5.1
  • Unitals in Hall Planes
  • 89
  • 5.2
  • Unitals in Semifield Planes
  • 97
  • 1.3
  • 5.3
  • Unitals in Nearfield Planes
  • 101
  • 5.4
  • Unitals Embedded in Nontranslation Planes
  • 103
  • 5.4.1
  • Figueroa Plane
  • 103
  • 5.4.2
  • Quadrics in Low Dimensions
  • Hughes Plane
  • 105
  • 6
  • Combinatorial Questions and Associated Configurations
  • 109
  • 6.1
  • Intersection Problems
  • 109
  • 6.2
  • Spreads and Packings
Control code
251890769
Dimensions
24 cm
Extent
xii, 193 pages
Isbn
9780387763644
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)251890769
Label
Unitals in projective planes, Susan Barwick, Gary Ebert
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 9
  • 117
  • 6.3
  • Related Combinatorial Structures
  • 121
  • 6.3.1
  • Inversive Planes
  • 121
  • 6.3.2
  • Arcs
  • 123
  • 1.4
  • 6.4
  • Unitals and Codes
  • 127
  • 7
  • Characterization Results
  • 133
  • 7.1
  • Characterizations of Unitals via Baer Sublines
  • 133
  • 7.2
  • Ovals and Ovoids
  • Proofs of Results from Section 7.1
  • 136
  • 7.3
  • Other Configurational Characterizations
  • 148
  • 7.3.1
  • Tallini Scafati Characterizations
  • 148
  • 7.3.2
  • Characterizations Using Feet
  • 12
  • 153
  • 7.3.3
  • Characterizations Using O'Nan Configurations
  • 161
  • 7.4
  • Characterizations Using the Quadratic Extension PG(4, q[superscript 2])
  • 164
  • 7.5
  • The Bose Representation of PG(2, q[superscript 2]) in PG(5, q)
  • 164
  • 1.5
  • 7.6
  • Group Theoretic Characterizations
  • 166
  • 8
  • Open Problems
  • 167
  • A Nomenclature of Unitals
  • 171
  • B
  • Group Theoretic Characterizations of Unitals
  • Some Linear Algebra
  • 173
  • 13
  • 2
  • Hermitian Curves and Unitals
  • 21
  • 1.1
  • 2.1
  • Nondegenerate Hermitian Curves
  • 21
  • 2.2
  • Degenerate Hermitian Curves and Baer Sublines
  • 24
  • 2.3
  • Unitals
  • 27
  • 3
  • Affine and Projective Geometries
  • Translation Planes
  • 33
  • 3.1
  • Translation Planes
  • 33
  • 3.2
  • Derivation
  • 34
  • 3.3
  • Spreads
  • 1
  • 36
  • 3.4
  • The Bruck-Bose Representation
  • 41
  • 3.4.1
  • The Bruck-Bose Construction
  • 41
  • 3.4.2
  • Baer Subplanes and Baer Sublines in Bruck-Bose
  • 43
  • 1.2
  • 3.4.3
  • Derivation in Bruck-Bose
  • 52
  • 3.4.4
  • Coordinates in Bruck-Bose
  • 53
  • 4
  • Unitals Embedded in Desarguesian Planes
  • 59
  • 4.1
  • Finite Fields
  • Buekenhout Constructions
  • 59
  • 4.2
  • Unitals Embedded in PG(2, q[superscript 2])
  • 66
  • 4.2.1
  • The Odd Characteristic Case
  • 66
  • 4.2.2
  • The Even Characteristic Case
  • 8
  • 79
  • 5
  • Unitals Embedded in Non-Desarguesian Planes
  • 89
  • 5.1
  • Unitals in Hall Planes
  • 89
  • 5.2
  • Unitals in Semifield Planes
  • 97
  • 1.3
  • 5.3
  • Unitals in Nearfield Planes
  • 101
  • 5.4
  • Unitals Embedded in Nontranslation Planes
  • 103
  • 5.4.1
  • Figueroa Plane
  • 103
  • 5.4.2
  • Quadrics in Low Dimensions
  • Hughes Plane
  • 105
  • 6
  • Combinatorial Questions and Associated Configurations
  • 109
  • 6.1
  • Intersection Problems
  • 109
  • 6.2
  • Spreads and Packings
Control code
251890769
Dimensions
24 cm
Extent
xii, 193 pages
Isbn
9780387763644
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)251890769

Library Locations

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      104 Ellis Library, Columbia, MO, 65201, US
      38.944377 -92.326537
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