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 second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kahler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the "Shafarevich conjecture". The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.
About Igor R. Shafarevich
Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.Details Book
Author  :  Igor R. Shafarevich 
Publisher  :  SpringerVerlag Berlin and Heidelberg GmbH 
Data Published  :  01 September 2013 
ISBN  :  3642380093 
EAN  :  9783642380099 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  262 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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