代数曲面和全纯向量丛

出版时间：2009-6  出版社：世界图书出版公司  作者：Robert Friedman  页数：328  
Tag标签：无  

内容概要

《代数曲面和全纯向量丛(英文版)》主要内容包括：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等。

书籍目录

PrefaceIntroduction1  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  Exercises2  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  Exercises3  B|ratlonal Geometry  Blowing up  The Castelnuovo criterion and factorization of birationa] morphisms  Minimal models  More general contractions  Exercises4  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  Exercises5  Some Examples of Surfaces  Rational ruled surfaces  General ruled surfaces  Linear systems of cubics  An introduction to K3 surfaces  Exercises6  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  Exercises7  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  Exercises8  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 Applications10  Classification of Algebraic Surfaces and of Stable BundlesReferencesIndex