Algebraic Surfaces / Edition 1

by V. Masek, Lucian Badescu

Overview

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.

Product Details

ISBN-13:	9781441931498
Publisher:	Springer New York
Publication date:	11/19/2010
Series:	Universitext Series
Edition description:	Softcover reprint of hardcover 1st ed. 2001
Pages:	270
Product dimensions:	9.21(w) x 6.14(h) x 0.57(d)

Table of Contents

* Intersection Theory and the Nakai-Moishezon Criterion
• The Hodge Index Theorem and the Intersection Matrix of a Fiber
• Criteria of Contractability and Rational Singularities
• Properties of Rational Singularities
• Noether's Formula, Picard Scheme, Albanese Variety, and Plurigenera
• Existence of Minimal Models
• Morphisms to a Curve, Elliptic and Quasielliptic Fibrations
• Canonical Dimension of an Elliptic or Quasielliptic Fibration
• The Classification Theorem According to Canonical Dimension
• Surfaces with Canonical Dimension Zero (char(k)=/2,3)
• Ruled Surfaces. The Noether-Tsen Criterion
• Minimal Models of Ruled Surfaces
• The Zariski decomposition and applications
• Appendix: Further reading

Editorial Reviews

From the reviews:

"This is an excellent textbook, very good for a graduate course in algebraic geometry. … The added exercises improve the quality of the book as a textbook. … many new references are added to the ones in the original edition. … I find very nice the last paragraph of every section, which contains bibliographic references; they reflect the author’s point of view on the history of these mathematical discoveries and they give useful hints for further readings, both to students and to advanced researchers." (Marco Andreatta, Mathematical Reviews, Issue 2001 k)

"The present book is a translation of an earlier Romanian text and one might ask: why publish it anew? … first of all it is the only existing monograph treating classification of algebraic surfaces in all characteristics in a reasonably self-contained manner. Secondly, it is very carefully written and gives all the necessary references. … My conclusion is that the monograph is a good introductory text for self-study or for a graduate course for anyone with the required background … ." (C. A. M. Peters, Nieuf Archief voor Wiskunde, Vol. 5/3 (4), 2002)

"The book under review is the translation into English of the Romanian original … . As this excellent textbook on general algebraic surfaces has not suffered loss from its actuality … it finally has conquered its deserved place within the international literature … . The exposition is very clear, thorough, rigorous, elegant, and positively creative. This makes the book into a still very valuable source … . Without any doubt, this is one of the very best books on algebraic surfaces, now as before." (Werner Kleinert, Zentralblatt MATH, Vol. 965, 2001)

"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 characteristics. This algebraic approach is one of the novelties in comparison to existing textbooks on the subject." (L’Enseignement Mathematique, Vol. 47 (1-2), 2001)

From the Publisher