Algebraic Geometry (book)
Template:Short description Script error: No such module "Infobox".Template:Template otherScript error: No such module "Check for unknown parameters".Template:Wikidata image Algebraic Geometry is an algebraic geometry textbook written by Robin Hartshorne and published by Springer-Verlag in 1977.[1]
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][4] 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.
Notes
References
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- ↑ MathSciNet lists more than 2500 citations of this book.
- ↑ Script error: No such module "citation/CS1". This is the professional’s handbook.
- ↑ Script error: No such module "citation/CS1". Hartshorne's classic book stands out as the canonical reference.
- ↑ Script error: No such module "Citation/CS1". ...has endured as the best one-volume treatment of this essential set of tools. Everyone in algebraic geometry eventually studies this book.