代数曲面和全纯向量丛
2009-6
世界图书出版公司
Robert Friedman
328
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《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。
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
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