The most important progress in the theory of complex surfaces has been made in regard of a better understanding of their differentiable structure (as real 4-manifolds), not at least in view of their appearance in mathematical physics.
In fact, in the two decades after the appearance of the first edition of the book, several crucial developments in the theory of complex surfaces have taken place, and the authors have taken the opportunity to update the original text by including some of those recent achievements. The book under review is the second, substantially enlarged edition of this standard text, this time with K. The first edition contained eight main chapters on about 300 pages, concluding with the classification of K3 surfaces and Enriques surfaces. Moreover, for almost twenty years it has been by far the most comprehensive textbook on complex surfaces from the modern point of view. Beauville, the first edition of the book under review offered the only up-to-date account of the subject in textbook form. Apart from the modern treatises on complex surfaces by I. The first edition of this well-known and very popular standard text on compact complex surfaces was published in 1984, back then written by W. This confinement mechanism guarantees that our results are robust. The runaway of Affleck-Harvey-Witten is however avoided by a non-perturbative confinement mechanism.
An important point is the existence of vector multiplet zero modes, unaccompanied by massless matter fields. We also make a conjecture for O(\beta) O ( β ), where we argue that the expansion truncates up to exponentially small corrections. The counting of BPS states in four-dimensional $,\beta^0 β − 2, β − 1, β 0.