ebook9783642380105d4325

Description

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‚Äôs 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, K√§hler 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.