Skip to main content
SpringerLink
Log in
Book cover

Algebraic Geometry

A First Course

  • Textbook
  • © 1992

Overview

Authors:
  1. Joe Harris

    1. Department of Mathematics, Harvard University, Cambridge, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Graduate Texts in Mathematics (GTM, volume 133)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 79.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (22 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Examples of Varieties and Maps

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Affine and Projective Varieties

      • Joe Harris
      Pages 3-16

    3. Regular Functions and Maps

      • Joe Harris
      Pages 17-31

    4. Cones, Projections, and More About Products

      • Joe Harris
      Pages 32-40

    5. Families and Parameter Spaces

      • Joe Harris
      Pages 41-47

    6. Ideals of Varieties, Irreducible Decomposition, and the Nullstellensatz

      • Joe Harris
      Pages 48-62

    7. Grassmannians and Related Varieties

      • Joe Harris
      Pages 63-71

    8. Rational Functions and Rational Maps

      • Joe Harris
      Pages 72-87

    9. More Examples

      • Joe Harris
      Pages 88-97

    10. Determinantal Varieties

      • Joe Harris
      Pages 98-113

    11. Algebraic Groups

      • Joe Harris
      Pages 114-129

  3. Attributes of Varieties

    1. Front Matter

      Pages 131-131
      Download chapter PDF

    2. Definitions of Dimension and Elementary Examples

      • Joe Harris
      Pages 133-150

    3. More Dimension Computations

      • Joe Harris
      Pages 151-162

    4. Hilbert Polynomials

      • Joe Harris
      Pages 163-173

    5. Smoothness and Tangent Spaces

      • Joe Harris
      Pages 174-185

    6. Gauss Maps, Tangential and Dual Varieties

      • Joe Harris
      Pages 186-199

    7. Tangent Spaces to Grassmannians

      • Joe Harris
      Pages 200-210

    8. Further Topics Involving Smoothness and Tangent Spaces

      • Joe Harris
      Pages 211-223
Back to top

Keywords

About this book

This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners.

Reviews

J. Harris

Algebraic Geometry

A First Course

"This book succeeds brilliantly by concentrating on a number of core topics (the rational normal curve, Veronese and Segre maps, quadrics, projections, Grassmannians, scrolls, Fano varieties, etc.) and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship."—MATHEMATICAL REVIEWS

Authors and Affiliations

  • Department of Mathematics, Harvard University, Cambridge, USA

    Joe Harris

Bibliographic Information

  • Book Title: Algebraic Geometry

  • Book Subtitle: A First Course

  • Authors: Joe Harris

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-2189-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1992

  • Hardcover ISBN: 978-0-387-97716-4Published: 17 September 1992

  • Softcover ISBN: 978-1-4419-3099-6Published: 01 December 2010

  • eBook ISBN: 978-1-4757-2189-8Published: 11 November 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XIX, 330

  • Topics: Algebraic Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation