Introduction to Algebraic Geometry (Graduate Studies in Mathematics) by Steven Dale Cutkosky (PDF)

Description

This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski’s main theorem, and Bertini’s theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

User’s Reviews

Editorial Reviews: Review The book is well written and self-contained; it contains both an introduction to the basics of the field and numerous advanced topics. –Luca Ugaglia, Mathematical Reviews About the Author Steven Dale Cutkosky, University of Missouri, Columbia, MO.

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