代數(shù)幾何

內(nèi)容概要

This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology. The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples. Then the methods of schemes and cohomology are developed in Chapters II and III, with emphasis on applications rather than excessive generality. The last two chapters of the book (IV and V) use these methods to study topics in the classical theory of algebraic curves and surfaces.

書籍目錄

Introduction CHAPTER I 　Varieties 　1 Affine Varieties 　2 Projective Varieties 　3 Morphisms 　4 Rational Maps 　5 Nonsingular Varieties 　6 Nonsingular Curves 　7 Intersections in Projective Space 　8 What Is Algebraic Geometry? CHAPTER II Schemes 　1 Sheaves 　2 Schemes 　3 First Properties of Schemes 　4 Separated and Proper Morphisms 　5 Sheaves of Modules 　6 Divisors 　7 Projective Morphisms 　8  Differentials　9  Formal SchemesCHAPTER III　Cohomology　1  Derived Functors　2  Cohomology of Sheaves　3  Cohomology of a Noetherian Affine Scheme　4  Cech Cohomology　5  The Cohomology of Projective Space　6  Ext Groups and Sheaves　7  The Serre Duality Theorem　8  Higher Direct images of Sheaves　9  Flat Morphisms　10  Smooth Morphisms　11  The Theorem on Formal Functions　12  The Semicontinuity TheoremCHAPTER IV　Curves　1  Riemann-Roch Theorem　2  Hurwitz's Theorem　3  Embeddings in Projective Space　4  Elliptic Carves　5  The Canonical Embedding　6  Classification of Curves in P3CHAPTER V　Surfaces　1  Geometry on a Surface　2  Ruled Surfaces　3  Monoidal Transformations　4  The Cubic Surface in P3　5  Birational Transformations　6  Classification of SurfacesAPPENDIX AAPPENDIX BAPPENDIX C BibliographyResults from AlgebraGlossary of NotationsIndex

圖書封面

圖書標(biāo)簽Tags

無

評論、評分、閱讀與下載

---

    代數(shù)幾何 PDF格式下載

---