代数曲面和全纯向量丛

Preface

Introduction

1 Curves on a Surface

Introduction

Invariants of a surface

Divisors on a surface

Adjunetion and arithmetic genus

The Riemann-Roch formula

Algebraic proof of the Hodge index theorem

Ample and nef divisors

Exercises

2 Coherent Sheaves

What is a coherent sheaf?

A rapid review of Chern classes for projective varieties

Rank 2 bundles and sub-line bundles

Elementary modifications

Singularities of coherent sheaves

Torsion free and reflexive sheaves

Double covers

Appendix： some commutative algebra

Exercises

3 B|ratlonal Geometry

Blowing up

The Castelnuovo criterion and factorization of birationa] morphisms

Minimal models

More general contractions

Exercises

4 Stability

Definition of Mumford-Takemoto stability

Examples for curves

Some examples of stable bundles on p2

Gieseker stability

Unstable and semlstable sheaves

Change of polarization

The differential geometry of stable vector bundles

Exercises

5 Some Examples of Surfaces

Rational ruled surfaces

General ruled surfaces

Linear systems of cubics

An introduction to K3 surfaces

Exercises

6 Vector Bundles over Ruled Surfaces

Suitable ample divisors

Ruled sur faces

A brief introduction to local and global moduli

A Zariski open subeet of the moduli space

Exercises

7 An Introduction to Elliptic Surfaces

Singular fibers

Singulex fibers of elliptic fibrations

lnvariants and the canonical bundle formula

Elliptic surfaces with a section and Weierstrass models

More general elliptic surfaces

The fundamental group

Exercises

8 Vector Bundles over Elliptic Surfaces

Stable bundles on singular curves

Stable bundles of odd fiber degree over elliptie surface*

A Zariski open subset of the modnii space

An overview of Donaldson invariants

The 2-dimensional invariant

……

9 Bogomolov's Inequality and Applications

10 Classification of Algebraic Surfaces and of Stable Bundles

References

Index

　　本书由世界图书出版公司出版，主要内容包括：AnIntroductiontoEllipticSurfaces、Singularfibers、Singulexfibersofellipticfibrations、lnvariantsandthecanonicalbundleformula、EllipticsurfaceswithasectionandWeierstrassmodels、Moregeneralellipticsurfaces、Thefundamentalgroup等。