By I. R. Shafarevich

ISBN-10: 0387519955

ISBN-13: 9780387519951

This quantity of the Encyclopaedia comprises elements. the 1st is dedicated to the speculation of curves, that are handled from either the analytic and algebraic issues of view. beginning with the fundamental notions of the speculation of Riemann surfaces the reader is lead into an exposition masking the Riemann-Roch theorem, Riemann's primary lifestyles theorem, uniformization and automorphic features. The algebraic fabric additionally treats algebraic curves over an arbitrary box and the relationship among algebraic curves and Abelian forms. the second one half is an advent to higher-dimensional algebraic geometry. the writer bargains with algebraic forms, the corresponding morphisms, the idea of coherent sheaves and, eventually, the idea of schemes. This ebook is a really readable creation to algebraic geometry and should be immensely precious to mathematicians operating in algebraic geometry and complicated research and particularly to graduate scholars in those fields.