Oberwolfach Seminars

Classification of Higher Dimensional Algebraic Varieties

Authors: Hacon, Christopher D., Kovács, Sándor

  • Introductory text to an advanced topic of active research

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  • ISBN 978-3-0346-0290-7
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About this Textbook

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.

Reviews

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)


Table of contents (16 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-0346-0290-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-0346-0289-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Classification of Higher Dimensional Algebraic Varieties
Authors
Series Title
Oberwolfach Seminars
Series Volume
41
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-0346-0290-7
DOI
10.1007/978-3-0346-0290-7
Softcover ISBN
978-3-0346-0289-1
Series ISSN
1661-237X
Edition Number
1
Number of Pages
220
Topics