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Basic Algebraic Geometry 2

Schemes and Complex Manifolds

  • Igor R. Shafarevich

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Book 2: Schemes and Varieties

    1. Front Matter
      Pages 1-1
    2. Igor R. Shafarevich
      Pages 3-47
    3. Igor R. Shafarevich
      Pages 49-111
  3. Book 3: Complex Algebraic Varieties and Complex Manifolds

    1. Front Matter
      Pages 113-113
    2. Igor R. Shafarevich
      Pages 115-148
    3. Igor R. Shafarevich
      Pages 149-199
    4. Igor R. Shafarevich
      Pages 201-228
  4. Back Matter
    Pages 229-262

About this book

Introduction

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 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.

Keywords

algebraic geometry complex algebraic varieties geometry schemes

Authors and affiliations

  • Igor R. Shafarevich
    • 1
  1. 1.Algebra SectionSteklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia

Bibliographic information