Translations of Mathematical Monographs 1994; 246 pp; softcover Volume: 136 Reprint/Revision History: reprinted with corrections 1997; fourth printing 2001 ISBN10: 0821809180 ISBN13: 9780821809181 List Price: US$88 Member Price: US$70.40 Order Code: MMONO/136.S
 Students often find, in setting out to study algebraic geometry, that most of the serious textbooks on the subject require knowledge of ring theory, field theory, local rings and transcendental field extensions, and even sheaf theory. Often the expected background goes well beyond college mathematics. This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting the necessary background along the way. Originally published in the Japanese in 1990, it presents a selfcontained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes and algebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces. Readership Senior undergraduates and graduate students. Reviews "The exposition of the subject is selfcontained and aims at graduate students who have no prior knowledge of the subject. Actually, a reader with only a basic knowledge of algebra may use this book to learn the language and foundations of algebraic geometry and subsequently may enjoy making first steps towards exploring the geometry of surfaces."  Mathematical Reviews Table of Contents Part I. Preliminaries  Theorem of Lüroth
 Theory of sheaves and cohomologies
Part II. Schemes and algebraic varieties  Affine schemes and algebraic varieties
 Schemes and algebraic varieties
 Projective schemes and projective algebraic varieties
 Nonsingular algebraic varieties
Part III. Algebraic surfaces  Algebraic curves
 Intersection theory on algebraic surfaces
 Pencils of curves
 The RiemannRoch Theorem for algebraic surfaces
 Minimal algebraic surfaces
 Ruled surfaces and rational surfaces
 Solutions to problems
 List of notation
 Bibliography
 Index
