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Synopsis
Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
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From the Back Cover
This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to the theory of moduli spaces. It includes topics such as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type.
The book is aimed at advanced graduate students and researchers in algebraic geometry.Review
From the reviews:
“The present text presents the proofs of many results surrounding the minimal model program (MMP) for higher-dimensional varieties. ... This text treats the subject in the great generality which is required for getting the most recent results. Hence, it is laden with terminology, all necessary for the modern researcher. ... As such, the text will be invaluable for those currently living off of survey articles trying to grasp recent advances in higher-dimensional geometry.” (Michael A. van Opstall, Mathematical Reviews, Issue 2011 f)
“The authors give a detailed account of these new results and the theory of compact moduli spaces of canonically polarised varieties. ... the book contains a considerable number of exercises as well as a chapter of hints to solve them. ... the authors have made quite an effort to write a text that is both an accessible introduction and a useful reference. ... I can only recommend it to researchers and advanced graduate students interested in this highly active field of mathematics.” (Andreas Höring, Zentralblatt MATH, Vol. 1204, 2011)
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- PublisherBirkhäuser
- Publication date2010
- ISBN 10 3034602898
- ISBN 13 9783034602891
- BindingPaperback
- LanguageEnglish
- Number of pages220
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Classification of Higher Dimensional Algebraic Varieties
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Classification of Higher Dimensional Algebraic Varieties (Oberwolfach Seminars, 41)
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Classification of Higher Dimensional Algebraic Varieties
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Classification of Higher Dimensional Algebraic Varieties
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to the theory of moduli spaces. It includes topics such as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type.The book is aimed at advanced graduate students and researchers in algebraic geometry. 200 pp. Englisch. Seller Inventory # 9783034602891
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Classification of Higher Dimensional Algebraic Varieties (Oberwolfach Seminars, 41)
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to the theory of moduli spaces. It includes topics such as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type.The book is aimed at advanced graduate students and researchers in algebraic geometry. Seller Inventory # 9783034602891
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Classification of Higher Dimensional Algebraic Varieties
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Introductory text to an advanced topic of active researchI Basics.- 1 Introduction.- 1.A. Classification.- 2 Preliminaries.- 2.A. Notation.- 2.B. Divisors.- 2.C. Reflexive sheaves.- 2.D. Cyclic covers.- 2.E. R-divisors in the relative setting.- 2.F. Van. Seller Inventory # 4317914
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