Algebraic surfaces代數(shù)表面

內(nèi)容概要

The main aim of this book is to present a completely algebraic approach to the Enriques¿ classification of smooth projective surfaces defined over an algebraically closed field of arbitrary characteristic. This algebraic approach is one of the novelties of this book among the other modern textbooks devoted to this subject. Two chapters on surface singularities are also included. The book can be useful as a textbook for a graduate course on surfaces, for researchers or graduate students in algebraic geometry, as well as those mathematicians working in algebraic geometry or related fields.

書籍目錄

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

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