Here is the first of a two-volume work offering an introduction to algebraic geometry. It makes the topic accessible to non-specialists and beginners and is suitable for undergraduates in mathematics as well as students of theoretical physics.

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.

Elementary introduction Author is one of the pioneers in the subject Author is outstanding mathematics writer Includes supplementary material: sn.pub/extras

Autorentext

Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.

Inhalt

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