Basic Algebraic Geometry 2

Schemes and Complex Manifolds

Authors: Shafarevich, Igor R.

  • Elementary introduction
  • Author is one of the pioneers in the subject
  • Author is outstanding mathematics writer
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  • ISBN 978-3-642-38010-5
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Hardcover $69.99
price for USA
  • ISBN 978-3-642-38009-9
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  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
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  • ISBN 978-3-662-51401-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this Textbook

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.''

The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''.

The style of  Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of  Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.

About the authors

Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.

Reviews

From the book reviews:

“I find the book wonderfully put together, and I am sure the reader will learn a lot, either from systematic study or from browsing particular topics. … In each chapter, the theorems, propositions, corollaries, examples, remarks, etc., each have their own independent numbering system, running consecutively throughout the chapter. This makes it a real chore to track any internal reference in the book.” (Robin Hartshorne, SIAM Review, Vol. 56 (4), December, 2014)

“This is the English translation of the third edition of the second volume of the author’s classic standard text ‘Basic algebraic geometry’ … . a perfect first introduction to various aspects of both classic and modern algebraic geometry as a whole. … the present second volume may serve as an excellent source for students and non-specialists to get themselves prepared for the study of more advanced books on abstract algebraic geometry, complex algebraic geometry, and moduli theory likewise.” (Werner Kleinert, zbMATH, Vol. 1277, 2014)


Table of contents (5 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-38010-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-3-642-38009-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA
  • ISBN 978-3-662-51401-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Basic Algebraic Geometry 2
Book Subtitle
Schemes and Complex Manifolds
Authors
Translated by
Reid, M.
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-642-38010-5
DOI
10.1007/978-3-642-38010-5
Hardcover ISBN
978-3-642-38009-9
Softcover ISBN
978-3-662-51401-6
Edition Number
3
Number of Pages
XIV, 262
Number of Illustrations and Tables
12 b/w illustrations
Additional Information
Original third Russian edition published in one volume by MCCME, Moscow, 2007
Topics