The first edition of "Compact Complex Surfaces" was published in 1984 and has become one of the most important books on the subject. In this second enlarged edition the major developments of the last 20 years have been incorporated. The Enriques-Kodaira classification is carried out in the spirit of Mori theory and many new developments have been added, including new analytic tools as well as new algebraic methods such as the theorems of Bogomolov and Reider and their applications. A new section is devoted to the stunning results achieved by the introduction of Donaldson and Seiberg-Witten invariants.
Table of Contents:
Introduction.- I. Preliminaries.- II. Curves on Surfaces.- III. Mappings of Surfaces.- IV. Some General Properties of Surfaces. V. Examples.- VI. The Enriques Kodaira Classification.- VII. Surfaces of General Type.- VIII. K3-Surfaces and Enriques Surfaces. IX. Topological and Differentiable Structure of Surfaces.- Bibliography.- Notation.- Index.
Review :
From the reviews of the second edition: "This volume is the second and substantially enlarged edition of the book that appeared for the first time in 1984. a ] The bibliography has been substantially extended, covering new developments. Already a classic in the field, this book is recommended both to mathematicians interested in this mathematical topic and physicists working in the modern theoretical physics." (EMS Newsletter, September, 2005)
"The book under review is the second, substantially enlarged edition a ] with K. Hulek as fourth co-author. a ] the bibliography has been updated and tremendously enlarged, thereby reflecting the vast activity in the field during the past twenty years. Now as before, the text is enriched by numerous instructive examples. a ] No doubt, this book remains a must for everyone dealing with complex algebraic surfaces, be it a student, an active researcher in complex geometry, or a mathematically ambitioned (quantum) physicist." (Werner Kleinert, Zentralblatt MATH, Vol. 1036 (11), 2004)
From the reviews of the second edition:
"This volume is the second and substantially enlarged edition of the book that appeared for the first time in 1984. ??? The bibliography has been substantially extended, covering new developments. Already a classic in the field, this book is recommended both to mathematicians interested in this mathematical topic and physicists working in the modern theoretical physics." (EMS Newsletter, September, 2005)
"The book under review is the second, substantially enlarged edition ??? with K. Hulek as fourth co-author. ??? the bibliography has been updated and tremendously enlarged, thereby reflecting the vast activity in the field during the past twenty years. Now as before, the text is enriched by numerous instructive examples. ??? No doubt, this book remains a must for everyone dealing with complex algebraic surfaces, be it a student, an active researcher in complex geometry, or a mathematically ambitioned (quantum) physicist." (Werner Kleinert, Zentralblatt MATH, Vol. 1036 (11), 2004)
