Algebraic Geometry (book)
Influential textbook about algebraic geometry, written by Robin Hartshorne
From Wikipedia, the free encyclopedia
Algebraic Geometry is an algebraic geometry textbook written by Robin Hartshorne and published by Springer-Verlag in 1977.[1]
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First edition | |
| Author | Robin Hartshorne |
|---|---|
| Language | English |
| Subject | Algebraic geometry |
| Genre | Textbook |
| Published | 1977 |
Importance
Although shorter synopses introducing scheme theory like Macdonald's Algebraic Geometry: Introduction to Schemes (1968) and Mumford's widely circulated but unpublished Red Book (1967) were available earlier, Hartshorne's Algebraic Geometry was the first comprehensive treatment of scheme theory written as a text intended to be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][4] Even so, it is considered to be notoriously difficult for beginners; reading it and working through the challenging exercises has been considered by some to be a rite-of-passage for students of algebraic geometry.[5] 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 Atiyah–Macdonald, Matsumura, and Zariski–Samuel 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.