The geometry of schemes / David Eisenbud, Joe Harris.

Includes bibliographical references (p. [279]-283) and index.

I. Basic Definitions. I.1. Affine Schemes. I.2. Schemes in General. I.3. Relative Schemes. I.4. The Functor of Points -- II. Examples. II.1. Reduced Schemes over Algebraically Closed Fields. II.2. Reduced Schemes over Non-Algebraically Closed Fields. II.3. Nonreduced Schemes. II.4. Arithmetic Schemes -- III. Projective Schemes. III.1. Attributes of Morphisms. III.2. Proj of a Graded Ring. III.3. Invariants of Projective Schemes -- IV. Classical Constructions. IV.1. Flexes of Plane Curves. IV.2. Blow-ups. IV.3. Fano Schemes. IV.4. Forms -- V. Local Constructions. V.1. Images. V.2. Resultants. V.3. Singular Schemes and Discriminants. V.4. Dual Curves. V.5. Double Point Loci -- VI. Schemes and Functors. VI.1. The Functor of Points. VI.2. Characterization of a Space by its Functor of Points.

"This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples and strives to show "what's going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course.

The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required."--BOOK JACKET.