Algebraic Geometry (book)

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Algebraic Geometry
Algebraic Geometry (book).jpg
First edition
Author Robin Hartshorne
LanguageEnglish
SubjectAlgebraic geometry
GenreTextbook
Published1977

Algebraic Geometry is an algebraic geometry textbook written by Robin Hartshorne and published by Springer-Verlag in 1977. [1]

Contents

Importance

It was the first extended treatment of scheme theory written as a text intended to be accessible to graduate students, and is considered to be the standard reference. [2] [3] . This book was cited when Hartshorne was awarded the Leroy P. Steele Prize for mathematical exposition in 1979.


Contents

The first chapter, titled "Varieties", deals with the classical algebraic geometry of varieties over algebraically closed fields. This chapter uses many classical results in commutative algebra, including Hilbert's Nullstellensatz, with the books by AtiyahMacdonald, Matsumura, and ZariskiSamuel as usual references. The second and the third chapters, "Schemes" and "Cohomology", form the technical heart of the book. The last two chapters, "Curves" and "Surfaces", respectively explore the geometry of 1- and 2-dimensional objects, using the tools developed in the chapters 2 and 3.

Notes

  1. MathSciNet lists more than 2500 citations of this book.
  2. Reid, Miles (1989). Undergraduate Algebraic Geometry. Cambridge University Press. p. 8.This is the professional’s handbook.
  3. Harris, Joe (1992). Algebraic Geometry: A First Course. Springer-Verlag. p. xii.Hartshorne's classic book stands out as the canonical reference.

References