The Resource Beauville surfaces and groups, Ingrid Bauer, Shelly Garion, Alina Vdovina, editors

Beauville surfaces and groups, Ingrid Bauer, Shelly Garion, Alina Vdovina, editors

Label
Beauville surfaces and groups
Title
Beauville surfaces and groups
Statement of responsibility
Ingrid Bauer, Shelly Garion, Alina Vdovina, editors
Contributor
Editor
Subject
Genre
Language
eng
Summary
This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces. It is the first time that these objects are discussed from the points of view of algebraic geometry as well as group theory. The book also includes various open problems and conjectures related to these surfaces. Beauville surfaces are a class of rigid regular surfaces of general type, which can be described in a purely algebraic combinatoric way. They play an important role in different fields of mathematics like algebraic geometry, group theory and number theory. The notion of Beauville surface was introduced by Fabrizio Catanese in 2000 and, after the first systematic study of these surfaces by Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there has been an increasing interest in the subject. These proceedings reflect the topics of the lectures presented during the workshop 'Beauville Surfaces and Groups 2012', held at Newcastle University, UK in June 2012. This conference brought together, for the first time, experts of different fields of mathematics interested in Beauville surfaces
Member of
Cataloging source
N$T
Dewey number
516.3/52
Illustrations
illustrations
Index
no index present
LC call number
QA571
LC item number
.B43 2015eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1967-
  • 2012
http://library.link/vocab/relatedWorkOrContributorName
  • Bauer, Ingrid C.
  • Garion, Shelly
  • Vdovina, Alina
  • Beauville Surfaces and Groups
Series statement
Springer Proceedings in Mathematics and Statistics
Series volume
volume 123
http://library.link/vocab/subjectName
  • Surfaces, Algebraic
  • Geometry, Algebraic
  • Group theory
  • MATHEMATICS
  • Geometry, Algebraic
  • Group theory
  • Surfaces, Algebraic
  • Mathematics
  • Algebraic Geometry
  • Group Theory and Generalizations
  • Number Theory
  • Algebraic geometry
  • Groups & group theory
  • Number theory
Label
Beauville surfaces and groups, Ingrid Bauer, Shelly Garion, Alina Vdovina, editors
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-13862-6
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Introduction; The Fundamental Group and Torsion Group of Beauville Surfaces; 1 Introduction; 2 Product-Quotient Surfaces; 3 The Fundamental Group; 4 Some Applications; References; Regular Algebraic Surfaces, Ramification Structures and Projective Planes; 1 Introduction; 2 Ramification Structures and Associated Surfaces; 2.1 Group Theoretical Structures; 2.2 From Ramification Structures to Algebraic Surfaces; 3 Groups with Special Presentations; 3.1 Ramification Structures for the Group in [15, Example 6.3]; 3.2 Ramification Structures for the Groups in [11, Example 3.3]
  • 3.3 Ramification Structures for the Group in [15, Example 6.4]3.4 Ramification Structures for the Groups of Theorem 3.1 with qge4; 3.5 Ramification Structures for the Group in [18, Example 2]; References; A Survey of Beauville p-Groups; 1 Introduction; 2 Definitions; 2.1 Beauville Structures; 2.2 p-Groups; 3 Beauville Groups in O'Brien Trees; 3.1 An Example; 3.2 Infinite Paths Through the O'Brien Trees; 4 Beauville Groups of Small Order; References; Strongly Real Beauville Groups; 1 Introduction; 2 The Finite Simple Groups; 3 Characteristically Simple Groups
  • 4 The Symmetric and Alternating Groups5 Almost Simple Groups; 6 Nilpotent Groups; References; Beauville Surfaces and Probabilistic Group Theory; 1 Beauville Surfaces and Beauville Structures; 2 Beauville Surfaces and Finite Simple Groups; 3 Hyperbolic Triangle Groups and Their Finite Quotients; 4 Beauville Structures for the Group `39`42`""613A``45`47`""603APSL2(q); 4.1 Sketch of the Proof of Theorem 10; 4.2 Proof of Theorem 7; 5 Beauville Structures for Finite Simple Groups; 5.1 Choosing Disjoint Conjugacy Classes; 5.2 Frobenius Formula and Witten's Zeta Function
  • 4 Beauville Structures in Cartesian Powers5 The Groups L2(q); 6 Counting Triples; 7 The Suzuki Groups; 8 The Small Ree Groups; 9 The Sporadic Simple Groups; 9.1 The Mathieu Groups; 9.2 Other Small Sporadic Simple Groups; 9.3 The Larger Sporadic Simple Groups; 10 The Groups L3(q) and U3(q); 10.1 L3(q); 10.2 U3(q); References; Remarks on Lifting Beauville Structures of Quasisimple Groups ; 1 Introduction; 2 Frattini Covers of Beauville Groups; 3 Semidirect Products with Beauville Structures; 4 Questions; References
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319138626
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
SpringerLink
Other control number
10.1007/978-3-319-13862-6
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)907641023
  • (OCoLC)ocn907641023
Label
Beauville surfaces and groups, Ingrid Bauer, Shelly Garion, Alina Vdovina, editors
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-13862-6
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Introduction; The Fundamental Group and Torsion Group of Beauville Surfaces; 1 Introduction; 2 Product-Quotient Surfaces; 3 The Fundamental Group; 4 Some Applications; References; Regular Algebraic Surfaces, Ramification Structures and Projective Planes; 1 Introduction; 2 Ramification Structures and Associated Surfaces; 2.1 Group Theoretical Structures; 2.2 From Ramification Structures to Algebraic Surfaces; 3 Groups with Special Presentations; 3.1 Ramification Structures for the Group in [15, Example 6.3]; 3.2 Ramification Structures for the Groups in [11, Example 3.3]
  • 3.3 Ramification Structures for the Group in [15, Example 6.4]3.4 Ramification Structures for the Groups of Theorem 3.1 with qge4; 3.5 Ramification Structures for the Group in [18, Example 2]; References; A Survey of Beauville p-Groups; 1 Introduction; 2 Definitions; 2.1 Beauville Structures; 2.2 p-Groups; 3 Beauville Groups in O'Brien Trees; 3.1 An Example; 3.2 Infinite Paths Through the O'Brien Trees; 4 Beauville Groups of Small Order; References; Strongly Real Beauville Groups; 1 Introduction; 2 The Finite Simple Groups; 3 Characteristically Simple Groups
  • 4 The Symmetric and Alternating Groups5 Almost Simple Groups; 6 Nilpotent Groups; References; Beauville Surfaces and Probabilistic Group Theory; 1 Beauville Surfaces and Beauville Structures; 2 Beauville Surfaces and Finite Simple Groups; 3 Hyperbolic Triangle Groups and Their Finite Quotients; 4 Beauville Structures for the Group `39`42`""613A``45`47`""603APSL2(q); 4.1 Sketch of the Proof of Theorem 10; 4.2 Proof of Theorem 7; 5 Beauville Structures for Finite Simple Groups; 5.1 Choosing Disjoint Conjugacy Classes; 5.2 Frobenius Formula and Witten's Zeta Function
  • 4 Beauville Structures in Cartesian Powers5 The Groups L2(q); 6 Counting Triples; 7 The Suzuki Groups; 8 The Small Ree Groups; 9 The Sporadic Simple Groups; 9.1 The Mathieu Groups; 9.2 Other Small Sporadic Simple Groups; 9.3 The Larger Sporadic Simple Groups; 10 The Groups L3(q) and U3(q); 10.1 L3(q); 10.2 U3(q); References; Remarks on Lifting Beauville Structures of Quasisimple Groups ; 1 Introduction; 2 Frattini Covers of Beauville Groups; 3 Semidirect Products with Beauville Structures; 4 Questions; References
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319138626
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
SpringerLink
Other control number
10.1007/978-3-319-13862-6
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)907641023
  • (OCoLC)ocn907641023

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