Overview
- Contains a rapid introduction to complex algebraic geometry Includes background material on topology, manifold theory and sheaf theory
- Analytic and algebraic approaches are developed somewhat in parallel
- Easy-going style will not intimidate newcomers to algebraic geometry
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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About this book
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
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Keywords
Table of contents (19 chapters)
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Analogies and Conjectures
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Front Matter
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Back Matter
Reviews
From the reviews:
“The book under review evolved from various courses in algebraic geometry the author taught at Purdue University. It is intended for graduate level courses on algebraic geometry over C. … Every section of each chapter ends with a series of exercises that complement the treated material, sometimes asking to give proofs of stated results. … This work can serve as a textbook in an introductory course in algebraic geometry with a strong emphasis on its transcendental aspects, or as a reference book on the subject.” (Pietro De Poi, Mathematical Reviews, June, 2013)
“Masterful mathematical expositors guide readers along a meaningful journey. … Every student should read this book first before grappling with any of those bibles. … This is an advanced book in its own right … . Arapura’s knack for doing things in the simplest possible way and explaining the ‘why’ makes for much easier reading than one might reasonably expect. Summing Up: Highly recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 50 (5), January, 2013)
“The book under review is a welcome addition to the literature on complex algebraic geometry. The approach chosen by the author balances the algebraic and transcendental approaches and unifies them by using sheaf theoretical methods. … This is a well-written text … with plenty of examples to illustrate the ideas being discussed.” (Felipe Zaldivar, The Mathematical Association of America, June, 2012)
“Book provides a very lucid, vivid, and versatile first introduction to algebraic geometry, with strong emphasis on its transcendental aspects. The author provides a broad panoramic view of the subject, illustrated with numerous instructive examples and interlarded with a wealth of hints for further reading. Indeed, the balance between rigor, intuition, and completeness in the presentation of the material is absolutely reasonable for suchan introductory course book, and … it may serve as an excellent guide to the great standard texts in the field.” (Werner Kleinert, Zentralblatt MATH, Vol. 1235, 2012)
Authors and Affiliations
About the author
Donu Arapura is a Professor of Mathematics at Purdue University. He received his Ph.D. from Columbia University in 1985. Dr. Arapura’s primary research includes algebraic geometry, and he has written and co-written several publications ranging from Hodge cycles to cohomology.
Bibliographic Information
Book Title: Algebraic Geometry over the Complex Numbers
Authors: Donu Arapura
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-1809-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Softcover ISBN: 978-1-4614-1808-5Published: 10 February 2012
eBook ISBN: 978-1-4614-1809-2Published: 15 February 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XII, 329
Number of Illustrations: 16 b/w illustrations, 1 illustrations in colour
Topics: Algebraic Geometry, Several Complex Variables and Analytic Spaces, Topology