Algebraic surfaces代数表面

书籍目录

Foreword to the English VersionPrefaceConventions and Notation1  Cohomological Intersection Theory and the Nakai-Moishezon Criterion of Ampleness2　The Hodge Index Theorem and the Structure of the Intersection Matrix of a Fiber3　Criteria of Contractability and Rational Singularities4　Properties of Rational Singularities5　Noether's Formula, the Picard Scheme, the Albanese Variety, and Plurigenera6　Existence of Minimal Models7　Morphisms from a Surface to a Curve. Elliptic and Quasielliptic Fibrations8　Canonical Dimension of an Elliptic or Quasielliptic Fibration9  The Classification Theorem According to Canonical Dimension10 Surfaces with Canonical Dimension Zero11 Ruled Surfaces. The Noether-Tsen Criterion12 Minimal Models of Ruled Surfaces13 Characterization of Ruled and Rational Surfaces14 Zariski Decomposition and Applications15 Appendix: Further ReadingReferencesIndex

作者简介

This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces. In fact, the classification of surfaces is the main scope of this book and the author presents the approach developed by Mumford and Bombieri. Chapters also cover the Zariski decomposition of effective divisors and graded algebras.

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