The Resource Iitaka Conjecture : an introduction, Osamu Fujino, (electronic book)
Iitaka Conjecture : an introduction, Osamu Fujino, (electronic book)
Resource Information
The item Iitaka Conjecture : an introduction, Osamu Fujino, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Iitaka Conjecture : an introduction, Osamu Fujino, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 The ambitious program for the birational classification of higherdimensional complex algebraic varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program. Now it is known that the heart of the Iitaka program is the Iitaka conjecture, which claims the subadditivity of the Kodaira dimension for fiber spaces. The main purpose of this book is to make the Iitaka conjecture more accessible. First, Viehweg's theory of weakly positive sheaves and big sheaves is described, and it is shown that the Iitaka conjecture follows from the Viehweg conjecture. Then, the Iitaka conjecture is proved in some special and interesting cases. A relatively simple new proof of Viehweg's conjecture is given for fiber spaces whose geometric generic fiber is of general type based on the weak semistable reduction theorem due to AbramovickKaru and the existence theorem of relative canonical models by BirkarCasciniHaconMcKernan. No deep results of the theory of variations of Hodge structure are needed. The Iitaka conjecture for fiber spaces whose base space is of general type is also proved as an easy application of Viehweg's weak positivity theorem, and the Viehweg conjecture for fiber spaces whose general fibers are elliptic curves is explained. Finally, the subadditivity of the logarithmic Kodaira dimension for morphisms of relative dimension one is proved. In this book, for the reader's convenience, known arguments as well as some results are simplified and generalized with the aid of relatively new techniques
 Language
 eng
 Extent
 1 online resource (138 p.).
 Note
 Description based upon print version of record
 Contents

 Intro  Preface  Acknowledgements  Contents  1 Overview  1.1 What is the Iitaka Program?  1.2 The Main Results  1.3 Historical Note  1.4 Precise Contents  1.5 References  2 Preliminaries  2.1 Notations, Terminology, and Conventions  2.2 Prerequisites  2.3 Preliminary Results  2.3.1 Basic Definitions  2.3.2 Iitaka Dimension and Kodaira Dimension  2.3.3 Cyclic Covers  2.3.4 Weakly Semistable Morphisms  2.3.5 Kollár's TorsionFreeness and Vanishing Theorem  2.3.6 On Abelian Varieties  2.3.7 Invariance of Plurigenera  2.3.8 Related Conjectures
 4.3 Fiber Spaces Whose Geometric Generic Fiber is of General Type  4.4 Elliptic Fibrations  4.5 Some Other Cases  4.5.1 Fiber Spaces Whose Base Space Has Maximal Albanese Dimension  4.5.2 Fiber Spaces Whose Geometric Generic Fiber Has a Good Minimal Model  4.5.3 Iitaka Conjecture in Positive Characteristic  5 overlineCn, n1 Revisited  5.1 Background of overlineCn, n1  5.2 overlineCn, n1  5.3 Some Related Results  5.3.1 Conjecture overlineCn, m for Affine Varieties, and so on  5.3.2 Subadditivity Due to KovácsPatakfalvi and Hashizume  5.4 Appendix: A Vanishing Lemma
 6 Appendices  6.1 C2,1  6.2 Conjectures ()n and (>)n  Appendix References  Index
 Isbn
 9789811533464
 Label
 Iitaka Conjecture : an introduction
 Title
 Iitaka Conjecture
 Title remainder
 an introduction
 Statement of responsibility
 Osamu Fujino
 Language
 eng
 Summary
 The ambitious program for the birational classification of higherdimensional complex algebraic varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program. Now it is known that the heart of the Iitaka program is the Iitaka conjecture, which claims the subadditivity of the Kodaira dimension for fiber spaces. The main purpose of this book is to make the Iitaka conjecture more accessible. First, Viehweg's theory of weakly positive sheaves and big sheaves is described, and it is shown that the Iitaka conjecture follows from the Viehweg conjecture. Then, the Iitaka conjecture is proved in some special and interesting cases. A relatively simple new proof of Viehweg's conjecture is given for fiber spaces whose geometric generic fiber is of general type based on the weak semistable reduction theorem due to AbramovickKaru and the existence theorem of relative canonical models by BirkarCasciniHaconMcKernan. No deep results of the theory of variations of Hodge structure are needed. The Iitaka conjecture for fiber spaces whose base space is of general type is also proved as an easy application of Viehweg's weak positivity theorem, and the Viehweg conjecture for fiber spaces whose general fibers are elliptic curves is explained. Finally, the subadditivity of the logarithmic Kodaira dimension for morphisms of relative dimension one is proved. In this book, for the reader's convenience, known arguments as well as some results are simplified and generalized with the aid of relatively new techniques
 Cataloging source
 EBLCP
 http://library.link/vocab/creatorName
 Fujino, Osamu
 Dewey number
 516.3/53
 Index
 index present
 LC call number
 QA564
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 SpringerBriefs in Mathematics
 http://library.link/vocab/subjectName
 Algebraic varieties
 Label
 Iitaka Conjecture : an introduction, Osamu Fujino, (electronic book)
 Note
 Description based upon print version of record
 Antecedent source
 file reproduced from an electronic resource
 Bibliography note
 Includes bibliographical references and index
 Contents

 Intro  Preface  Acknowledgements  Contents  1 Overview  1.1 What is the Iitaka Program?  1.2 The Main Results  1.3 Historical Note  1.4 Precise Contents  1.5 References  2 Preliminaries  2.1 Notations, Terminology, and Conventions  2.2 Prerequisites  2.3 Preliminary Results  2.3.1 Basic Definitions  2.3.2 Iitaka Dimension and Kodaira Dimension  2.3.3 Cyclic Covers  2.3.4 Weakly Semistable Morphisms  2.3.5 Kollár's TorsionFreeness and Vanishing Theorem  2.3.6 On Abelian Varieties  2.3.7 Invariance of Plurigenera  2.3.8 Related Conjectures
 4.3 Fiber Spaces Whose Geometric Generic Fiber is of General Type  4.4 Elliptic Fibrations  4.5 Some Other Cases  4.5.1 Fiber Spaces Whose Base Space Has Maximal Albanese Dimension  4.5.2 Fiber Spaces Whose Geometric Generic Fiber Has a Good Minimal Model  4.5.3 Iitaka Conjecture in Positive Characteristic  5 overlineCn, n1 Revisited  5.1 Background of overlineCn, n1  5.2 overlineCn, n1  5.3 Some Related Results  5.3.1 Conjecture overlineCn, m for Affine Varieties, and so on  5.3.2 Subadditivity Due to KovácsPatakfalvi and Hashizume  5.4 Appendix: A Vanishing Lemma
 6 Appendices  6.1 C2,1  6.2 Conjectures ()n and (>)n  Appendix References  Index
 Dimensions
 unknown
 Extent
 1 online resource (138 p.).
 File format
 one file format
 Form of item
 online
 Isbn
 9789811533464
 Level of compression
 unknown
 Other control number
 10.1007/978981153
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
 System control number

 on1151190204
 (OCoLC)1151190204
 Label
 Iitaka Conjecture : an introduction, Osamu Fujino, (electronic book)
 Note
 Description based upon print version of record
 Antecedent source
 file reproduced from an electronic resource
 Bibliography note
 Includes bibliographical references and index
 Contents

 Intro  Preface  Acknowledgements  Contents  1 Overview  1.1 What is the Iitaka Program?  1.2 The Main Results  1.3 Historical Note  1.4 Precise Contents  1.5 References  2 Preliminaries  2.1 Notations, Terminology, and Conventions  2.2 Prerequisites  2.3 Preliminary Results  2.3.1 Basic Definitions  2.3.2 Iitaka Dimension and Kodaira Dimension  2.3.3 Cyclic Covers  2.3.4 Weakly Semistable Morphisms  2.3.5 Kollár's TorsionFreeness and Vanishing Theorem  2.3.6 On Abelian Varieties  2.3.7 Invariance of Plurigenera  2.3.8 Related Conjectures
 4.3 Fiber Spaces Whose Geometric Generic Fiber is of General Type  4.4 Elliptic Fibrations  4.5 Some Other Cases  4.5.1 Fiber Spaces Whose Base Space Has Maximal Albanese Dimension  4.5.2 Fiber Spaces Whose Geometric Generic Fiber Has a Good Minimal Model  4.5.3 Iitaka Conjecture in Positive Characteristic  5 overlineCn, n1 Revisited  5.1 Background of overlineCn, n1  5.2 overlineCn, n1  5.3 Some Related Results  5.3.1 Conjecture overlineCn, m for Affine Varieties, and so on  5.3.2 Subadditivity Due to KovácsPatakfalvi and Hashizume  5.4 Appendix: A Vanishing Lemma
 6 Appendices  6.1 C2,1  6.2 Conjectures ()n and (>)n  Appendix References  Index
 Dimensions
 unknown
 Extent
 1 online resource (138 p.).
 File format
 one file format
 Form of item
 online
 Isbn
 9789811533464
 Level of compression
 unknown
 Other control number
 10.1007/978981153
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
 System control number

 on1151190204
 (OCoLC)1151190204
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