Basic Algebraic Geometry 1 [electronic resource] : Varieties in Projective Space / by Igor R. Shafarevich.

Preface -- Book 1. Varieties in Projective Space: Chapter 1. Basic Notions -- Chapter II. Local Properties -- Chapter III. Divisors and Differential Forms -- Chapter IV. Intersection Numbers -- Algebraic Appendix -- References -- Index.

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction  to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.