Algebraic Geometry

First edition
Author	Robin Hartshorne
Language	English
Subject	Algebraic geometry
Genre	Textbook
Published	1977

Algebraic Geometry is analgebraic geometrytextbook written byRobin Hartshorne and published bySpringer-Verlag in 1977.^[1]

It was the first extended treatment ofscheme theory written as a text intended to be accessible to graduate students, and is considered to be the standard reference.^[2][3][4] This book was cited when Hartshorne was awarded theLeroy P. Steele Prize for mathematical exposition in 1979.

The first chapter, titled "Varieties", deals with the classical algebraic geometry ofvarieties overalgebraically closed fields. This chapter uses many classical results incommutative algebra, includingHilbert'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.

• Hartshorne, Robin (1977).Algebraic Geometry. Berlin, New York:Springer-Verlag.doi:10.1007/978-1-4757-3849-0.ISBN 978-0-387-90244-9.MR 0463157.Zbl 0367.14001.
• Shatz, Stephen S. (1979),"Review: Robin Hartshorne,Algebraic geometry",Bull. Amer. Math. Soc. (N.S.),1 (3):553–560,doi:10.1090/S0273-0979-1979-14618-4

• Graduate Texts in Mathematics
• 1977 non-fiction books
• Algebraic geometry
• Mathematics textbooks
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