Algebraic surfaces

by Bădescu, Lucian

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Title Statements

Full title :Algebraic surfaces / Lucian Bădescu ; translated by Vladimir Maşek.

Summary

"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 in comparison to existing textbooks on the subject. In the new edition of this book, two chapters as well as exercises at the end of each chapter have been added. One new chapter deals with various applications of the Zariski decomposition of an effective divisor, and the other discusses some results on surfaces that were found after the publication of the first edition. For a reader who has completed a first course in algebraic geometry, the present book is completely self-contained. It can be used as a textbook for a graduate course on surfaces or as a resource for researchers and graduate students in algebraic geometry and related fields."--Jacket.

Edition Statements

Publication Date:©2001.

Publication Statements

Publisher(s):Springer
Place of Publication:New York
Language:eng
Publication Date:©2001.

The Physical Object

Description:x, 258 pages : : illustrations ; : 25 cm.

Edition Identifiers

ISBN:0387986685, 9780387986685, 144193149X, 9781441931498
oclc:ocm44713308
LC Classification:QA571
Dewey Decimal:516.3/52

1. Cohomological Intersection Theory and the Nakai-Moishezon criterion of ampleness -- 2. The Hodge Index Theorem and the structure of the intersection matrix of a fiber -- 3. Criteria of contractability and rational singularities -- 4. Properties of rational singularities -- 5. Noether's formula, the Picard scheme, the Albanese variety, and Plurigenera -- 6. Existence of minimal models -- 7. Morphisms from a surface to a curve. Elliptic and quasielliptic fibrations -- 8. Canonical dimension of an elliptic or quasielliptic fibration -- 9. The classification theorem according to canonical dimension -- 10. Surfaces with canonical dimension zero -- 11. Ruled surface. The Noether-Tsen criterion -- 12. Minimal models of ruled surfaces -- 13. Characterization of ruled and rational surfaces -- 14. Zariski decomposition and applications -- 15. Appendix: further reading.