Algebraic Geometry - R. Hartshorne
This book provides an introduction to abstract algebraic geometry using
the methods of schemes and cohomology. The main objects of study are
algebraic varieties in an affine or projective space over an algebraically
closed field; these are introduced in Chapter I, to establish a number of
basic concepts and examples. Then the methods of schemes and
cohomology are developed in Chapters II and III, with emphasis on appli-
cations rather than excessive generality. The last two chapters of the book
(IV and V) use these methods to study topics in the classical theory of
algebraic curves and surfaces.
The prerequisites for this approach to algebraic geometry are results
from commutative algebra, which are stated as needed, and some elemen-
tary topology. No complex analysis or differential geometry is necessary.
There are more than four hundred exercises throughout the book, offering
specific examples as well as more specialized topics not treated in the
main text. Three appendices present brief accounts of some areas of
current research.
This book can be used as a textbook for an introductory course in
algebraic geometry, following a basic graduate course in algebra. I re-
cently taught this material in a five-quarter sequence at Berkeley, with
roughly one chapter per quarter. Or one can use Chapter I alone for a
short course. A third possibility worth considering is to study Chapter I,
and then proceed directly to Chapter IV, picking up only a few definitions
from Chapters II and III and assuming the statement of the Riemann-
Roch theorem for curves. This leads to interesting material quickly, and
may provide bettet motivation for tackling Chapters II and III later.
- Hardcover: 512 pages
- Publisher: Springer (December 19, 1977)
- Language: English
- ISBN-10: 0387902449
- ISBN-13: 978-0387902449
- Product Dimensions: 6.1 x 1.1 x 9.2 inches
This book provides an introduction to abstract algebraic geometry using
the methods of schemes and cohomology. The main objects of study are
algebraic varieties in an affine or projective space over an algebraically
closed field; these are introduced in Chapter I, to establish a number of
basic concepts and examples. Then the methods of schemes and
cohomology are developed in Chapters II and III, with emphasis on appli-
cations rather than excessive generality. The last two chapters of the book
(IV and V) use these methods to study topics in the classical theory of
algebraic curves and surfaces.
The prerequisites for this approach to algebraic geometry are results
from commutative algebra, which are stated as needed, and some elemen-
tary topology. No complex analysis or differential geometry is necessary.
There are more than four hundred exercises throughout the book, offering
specific examples as well as more specialized topics not treated in the
main text. Three appendices present brief accounts of some areas of
current research.
This book can be used as a textbook for an introductory course in
algebraic geometry, following a basic graduate course in algebra. I re-
cently taught this material in a five-quarter sequence at Berkeley, with
roughly one chapter per quarter. Or one can use Chapter I alone for a
short course. A third possibility worth considering is to study Chapter I,
and then proceed directly to Chapter IV, picking up only a few definitions
from Chapters II and III and assuming the statement of the Riemann-
Roch theorem for curves. This leads to interesting material quickly, and
may provide bettet motivation for tackling Chapters II and III later.
