Synopses & Reviews
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, Kähler geometry and Hodge theory. It raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture. The style of Volume II and its minimal prerequisites make it to a large extent independent of Volume I, and accessible to beginning graduate students in mathematics and in theoretical physics.
Synopsis
Basic Algebraic Geometry II
Synopsis
Basic Algebraic Geometry II
Synopsis
Basic Algebraic Geometry II
Synopsis
Basic Algebraic Geometry II
Synopsis
Basic Algebraic Geometry II is a revised edition of Shafarevich's well-known introductory book on algebraic varieties and complex manifolds. It can be read independently of Volume I and is suitable for graduate students in mathematics and theoretical physics.
Synopsis
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, Kähler geometry and Hodge theory. The final section raises
About the Author
Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.
Table of Contents
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.