TY - BOOK ID - 6420626 TI - Algebraic geometry I : algebraic curves, algebraic manifolds and schemes AU - Danilov, Vladimir Ivanovič AU - Šafarevič, Igor' Rostislavovič AU - Šokurov, Vâčeslav Vladimirovič PY - 1994 VL - 23 SN - 3540519955 9783540519959 0387519955 9780387519951 PB - Berlin : Springer, DB - UniCat KW - Curves, Algebraic. KW - Manifolds (Mathematics) KW - Schemes (Algebraic geometry) KW - Manifolds (Mathematics). KW - Schemes (Algebraic geometry). UR - https://www.unicat.be/uniCat?func=search&query=sysid:6420626 AB - This book consists of two parts. The first is devoted to the theory of curves, which are treated from both the analytic and algebraic points of view. Starting with the basic notions of the theory of Riemann surfaces the reader is lead into an exposition covering the Riemann-Roch theorem, Riemann's fundamental existence theorem, uniformization and automorphic functions. The algebraic material also treats algebraic curves over an arbitrary field and the connection between algebraic curves and Abelian varieties. The second part is an introduction to higher-dimensional algebraic geometry. The author deals with algebraic varieties, the corresponding morphisms, the theory of coherent sheaves and, finally, the theory of schemes. This book is a very readable introduction to algebraic geometry and will be immensely useful to mathematicians working in algebraic geometry and complex analysis and especially to graduate students in these fields. ER -