Algebraic Geometry over the Complex Numbers

  • Donu Arapura

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction through Examples

    1. Front Matter
      Pages 1-1
    2. Donu Arapura
      Pages 3-17
  3. Sheaves and Geometry

    1. Front Matter
      Pages 19-19
    2. Donu Arapura
      Pages 21-47
    3. Donu Arapura
      Pages 49-78
    4. Donu Arapura
      Pages 79-96
    5. Donu Arapura
      Pages 97-115
    6. Donu Arapura
      Pages 117-136
    7. Donu Arapura
      Pages 137-153
  4. Hodge Theory

    1. Front Matter
      Pages 155-155
    2. Donu Arapura
      Pages 157-167
    3. Donu Arapura
      Pages 169-177
    4. Donu Arapura
      Pages 179-188
    5. Donu Arapura
      Pages 189-201
    6. Donu Arapura
      Pages 203-221
    7. Donu Arapura
      Pages 223-236
    8. Donu Arapura
      Pages 237-251
  5. Coherent Cohomology

    1. Front Matter
      Pages 253-253
    2. Donu Arapura
      Pages 255-264

About this book


This textbook is a strong addition to existing introductory literature on algebraic geometry. The author’s treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields.

Unique features of this textbook:

- 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 The presentation is easy going, elementary, and well illustrated with examples.

“Algebraic Geometry over the Complex Numbers” is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory.


Hodge theory algebraic geometry algebraic variety complex manifold complex numbers sheaf sheaf-theoretic method

Authors and affiliations

  • Donu Arapura
    • 1
  1. 1., Department of MathematicsPurdue UniversityWest LafayetteUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1808-5
  • Online ISBN 978-1-4614-1809-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site