Borrow it
 Architecture Library
 Bizzell Memorial Library
 Boorstin Collection
 Chinese Literature Translation Archive
 Engineering Library
 Fine Arts Library
 Harry W. Bass Business History Collection
 History of Science Collections
 John and Mary Nichols Rare Books and Special Collections
 Library Service Center
 Price College Digital Library
 Western History Collections
The Resource Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource)
Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource)
Resource Information
The item Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This book is based on courses given at Columbia University on vector bun dles (1988) and on the theory of algebraic surfaces (1992), as well as lectures in the Park City lIAS Mathematics Institute on 4manifolds and Donald son invariants. The goal of these lectures was to acquaint researchers in 4manifold topology with the classification of algebraic surfaces and with methods for describing moduli spaces of holomorphic bundles on algebraic surfaces with a view toward computing Donaldson invariants. Since that time, the focus of 4manifold topology has shifted dramatically, at first be cause topological methods have largely superseded algebrogeometric meth ods in computing Donaldson invariants, and more importantly because of and Witten, which have greatly sim the new invariants defined by Seiberg plified the theory and led to proofs of the basic conjectures concerning the 4manifold topology of algebraic surfaces. However, the study of algebraic surfaces and the moduli spaces of bundles on them remains a fundamen tal problem in algebraic geometry, and I hope that this book will make this subject more accessible. Moreover, the recent applications of Seiberg Witten theory to symplectic 4manifolds suggest that there is room for yet another treatment of the classification of algebraic surfaces. In particular, despite the number of excellent books concerning algebraic surfaces, I hope that the half of this book devoted to them will serve as an introduction to the subject
 Language

 eng
 eng
 Edition
 1st ed. 1998.
 Extent
 1 online resource (IX, 329 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 1 Curves on a Surface
 Invariants of a surface
 Divisors on a surface
 Adjunction and arithmetic genus
 The RiemannRoch formula
 Algebraic proof of the Hodge index theorem
 Ample and nef divisors
 Exercises
 2 Coherent Sheaves
 What is a coherent sheaf?
 A rapid review of Chern classes for projective varieties
 Rank 2 bundles and subline bundles
 Elementary modifications
 Singularities of coherent sheaves
 Torsion free and reflexive sheaves
 Double covers
 Appendix: some commutative algebra
 Exercises
 3 Birational Geometry
 Blowing up
 The Castelnuovo criterion and factorization of birational morphisms
 Minimal models
 More general contractions
 Exercises
 4 Stability
 Definition of MumfordTakemoto stability
 Examples for curves
 Some examples of stable bundles on ?2
 Gieseker stability
 Unstable and semistable sheaves
 Change of polarization
 The differential geometry of stable vector bundles
 Exercises
 5 Some Examples of Surfaces
 Rational ruled surfaces
 General ruled surfaces
 Linear systems of cubics
 An introduction toK3 surfaces
 Exercises
 6 Vector Bundles over Ruled Surfaces
 Suitable ample divisors
 Ruled surfaces
 A brief introduction to local and global moduli
 A Zariski open subset of the moduli space
 Exercises
 7 An Introduction to Elliptic Surfaces
 Singular fibers
 Singular fibers of elliptic fibrations
 Invariants and the canonical bundle formula
 Elliptic surfaces with a section and Weierstrass models
 More general elliptic surfaces
 The fundamental group
 Exercises
 8 Vector Bundles over Elliptic Surfaces
 Stable bundles on singular curves
 Stable bundles of odd fiber degree over elliptic surfaces
 A Zariski open subset of the moduli space
 An overview of Donaldson invariants
 The 2dimensional invariant
 Moduli spaces via extensions
 Vector bundles with trivial determinant
 Even fiber degree and multiple fibers
 Exercises
 9 Bogomolov’s Inequality and Applications
 Statement of the theorem
 The theorems of Bombieri and Reider
 The proof of Bogomolov’s theorem
 Symmetric powers of vector bundles on curves
 Restriction theorems
 Appendix: Galois descent theory
 Exercises
 10 Classification of Algebraic Surfaces and of Stable
 Bundles
 Outline of the classification of surfaces
 Proof of Castelnuovo’s theorem
 The Albanese map
 Proofs of the classification theorems for surfaces
 The CastelnuovodeFranchis theorem
 Classification of threefolds
 Classification of vector bundles
 Exercises
 References
 Isbn
 9781461216889
 Label
 Algebraic Surfaces and Holomorphic Vector Bundles
 Title
 Algebraic Surfaces and Holomorphic Vector Bundles
 Statement of responsibility
 by Robert Friedman
 Language

 eng
 eng
 Summary
 This book is based on courses given at Columbia University on vector bun dles (1988) and on the theory of algebraic surfaces (1992), as well as lectures in the Park City lIAS Mathematics Institute on 4manifolds and Donald son invariants. The goal of these lectures was to acquaint researchers in 4manifold topology with the classification of algebraic surfaces and with methods for describing moduli spaces of holomorphic bundles on algebraic surfaces with a view toward computing Donaldson invariants. Since that time, the focus of 4manifold topology has shifted dramatically, at first be cause topological methods have largely superseded algebrogeometric meth ods in computing Donaldson invariants, and more importantly because of and Witten, which have greatly sim the new invariants defined by Seiberg plified the theory and led to proofs of the basic conjectures concerning the 4manifold topology of algebraic surfaces. However, the study of algebraic surfaces and the moduli spaces of bundles on them remains a fundamen tal problem in algebraic geometry, and I hope that this book will make this subject more accessible. Moreover, the recent applications of Seiberg Witten theory to symplectic 4manifolds suggest that there is room for yet another treatment of the classification of algebraic surfaces. In particular, despite the number of excellent books concerning algebraic surfaces, I hope that the half of this book devoted to them will serve as an introduction to the subject
 http://library.link/vocab/creatorName
 Friedman, Robert
 Dewey number
 516.35
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 2F8BfX0jeEs
 Image bit depth
 0
 Language note
 English
 LC call number
 QA564609
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Universitext,
 http://library.link/vocab/subjectName

 Geometry, algebraic
 Algebraic Geometry
 Label
 Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 Curves on a Surface  Invariants of a surface  Divisors on a surface  Adjunction and arithmetic genus  The RiemannRoch formula  Algebraic proof of the Hodge index theorem  Ample and nef divisors  Exercises  2 Coherent Sheaves  What is a coherent sheaf?  A rapid review of Chern classes for projective varieties  Rank 2 bundles and subline bundles  Elementary modifications  Singularities of coherent sheaves  Torsion free and reflexive sheaves  Double covers  Appendix: some commutative algebra  Exercises  3 Birational Geometry  Blowing up  The Castelnuovo criterion and factorization of birational morphisms  Minimal models  More general contractions  Exercises  4 Stability  Definition of MumfordTakemoto stability  Examples for curves  Some examples of stable bundles on ?2  Gieseker stability  Unstable and semistable sheaves  Change of polarization  The differential geometry of stable vector bundles  Exercises  5 Some Examples of Surfaces  Rational ruled surfaces  General ruled surfaces  Linear systems of cubics  An introduction toK3 surfaces  Exercises  6 Vector Bundles over Ruled Surfaces  Suitable ample divisors  Ruled surfaces  A brief introduction to local and global moduli  A Zariski open subset of the moduli space  Exercises  7 An Introduction to Elliptic Surfaces  Singular fibers  Singular fibers of elliptic fibrations  Invariants and the canonical bundle formula  Elliptic surfaces with a section and Weierstrass models  More general elliptic surfaces  The fundamental group  Exercises  8 Vector Bundles over Elliptic Surfaces  Stable bundles on singular curves  Stable bundles of odd fiber degree over elliptic surfaces  A Zariski open subset of the moduli space  An overview of Donaldson invariants  The 2dimensional invariant  Moduli spaces via extensions  Vector bundles with trivial determinant  Even fiber degree and multiple fibers  Exercises  9 Bogomolov’s Inequality and Applications  Statement of the theorem  The theorems of Bombieri and Reider  The proof of Bogomolov’s theorem  Symmetric powers of vector bundles on curves  Restriction theorems  Appendix: Galois descent theory  Exercises  10 Classification of Algebraic Surfaces and of Stable  Bundles  Outline of the classification of surfaces  Proof of Castelnuovo’s theorem  The Albanese map  Proofs of the classification theorems for surfaces  The CastelnuovodeFranchis theorem  Classification of threefolds  Classification of vector bundles  Exercises  References
 Dimensions
 unknown
 Edition
 1st ed. 1998.
 Extent
 1 online resource (IX, 329 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461216889
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461216889
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089656
 (SSID)ssj0001295789
 (PQKBManifestationID)11757436
 (PQKBTitleCode)TC0001295789
 (PQKBWorkID)11346606
 (PQKB)10528956
 (DEHe213)9781461216889
 (MiAaPQ)EBC3077009
 (EXLCZ)993400000000089656
 Label
 Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 Curves on a Surface  Invariants of a surface  Divisors on a surface  Adjunction and arithmetic genus  The RiemannRoch formula  Algebraic proof of the Hodge index theorem  Ample and nef divisors  Exercises  2 Coherent Sheaves  What is a coherent sheaf?  A rapid review of Chern classes for projective varieties  Rank 2 bundles and subline bundles  Elementary modifications  Singularities of coherent sheaves  Torsion free and reflexive sheaves  Double covers  Appendix: some commutative algebra  Exercises  3 Birational Geometry  Blowing up  The Castelnuovo criterion and factorization of birational morphisms  Minimal models  More general contractions  Exercises  4 Stability  Definition of MumfordTakemoto stability  Examples for curves  Some examples of stable bundles on ?2  Gieseker stability  Unstable and semistable sheaves  Change of polarization  The differential geometry of stable vector bundles  Exercises  5 Some Examples of Surfaces  Rational ruled surfaces  General ruled surfaces  Linear systems of cubics  An introduction toK3 surfaces  Exercises  6 Vector Bundles over Ruled Surfaces  Suitable ample divisors  Ruled surfaces  A brief introduction to local and global moduli  A Zariski open subset of the moduli space  Exercises  7 An Introduction to Elliptic Surfaces  Singular fibers  Singular fibers of elliptic fibrations  Invariants and the canonical bundle formula  Elliptic surfaces with a section and Weierstrass models  More general elliptic surfaces  The fundamental group  Exercises  8 Vector Bundles over Elliptic Surfaces  Stable bundles on singular curves  Stable bundles of odd fiber degree over elliptic surfaces  A Zariski open subset of the moduli space  An overview of Donaldson invariants  The 2dimensional invariant  Moduli spaces via extensions  Vector bundles with trivial determinant  Even fiber degree and multiple fibers  Exercises  9 Bogomolov’s Inequality and Applications  Statement of the theorem  The theorems of Bombieri and Reider  The proof of Bogomolov’s theorem  Symmetric powers of vector bundles on curves  Restriction theorems  Appendix: Galois descent theory  Exercises  10 Classification of Algebraic Surfaces and of Stable  Bundles  Outline of the classification of surfaces  Proof of Castelnuovo’s theorem  The Albanese map  Proofs of the classification theorems for surfaces  The CastelnuovodeFranchis theorem  Classification of threefolds  Classification of vector bundles  Exercises  References
 Dimensions
 unknown
 Edition
 1st ed. 1998.
 Extent
 1 online resource (IX, 329 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461216889
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461216889
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089656
 (SSID)ssj0001295789
 (PQKBManifestationID)11757436
 (PQKBTitleCode)TC0001295789
 (PQKBWorkID)11346606
 (PQKB)10528956
 (DEHe213)9781461216889
 (MiAaPQ)EBC3077009
 (EXLCZ)993400000000089656
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
Embed (Experimental)
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/AlgebraicSurfacesandHolomorphicVector/xOnw50i_dmk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/AlgebraicSurfacesandHolomorphicVector/xOnw50i_dmk/">Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/AlgebraicSurfacesandHolomorphicVector/xOnw50i_dmk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/AlgebraicSurfacesandHolomorphicVector/xOnw50i_dmk/">Algebraic Surfaces and Holomorphic Vector Bundles, by Robert Friedman, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>