A Series of Modern Surveys in Mathematics Volume 4: Compact Complex Surfaces: Second Enlarged Edition

In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac­ cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.

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)

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)