Author	Shafarevich, Igor R. author
Title	Basic Algebraic Geometry 2 [electronic resource] : Schemes and Complex Manifolds / by Igor R. Shafarevich
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
Edition	3rd ed. 2013
Connect to	http://dx.doi.org/10.1007/978-3-642-38010-5
Descript	XIV, 262 p. 12 illus. online resource

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, Kรคhler geometry and Hodge theory. The final section raisesย an important problem in uniformising higher dimensional varieties that has been widely studied as the ̀S̀hafarevich conjecture''. The style ofย  Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent ofย  Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics

Preface -- Book 1. Varieties in Projective Space: Chapter I. Basic Notions -- Chapter II. Local Properties -- Chapter III. Divisors and Differential Forms -- Chapter IV. Intersection Numbers -- Algebraic Appendix -- References -- Index

1. Mathematics
2. Geometry
3. algebraic
4. Mathematics
5. Algebraic Geometry
6. Theoretical
7. Mathematical and Computational Physics