Within the 19 years which handed because the first variation used to be released, a number of very important advancements have taken position within the concept of surfaces. the main sensational one issues the differentiable constitution of surfaces. 20 years in the past little or no was once identified approximately differentiable constructions on 4-manifolds, yet meanwhile Donaldson at the one hand and Seiberg and Witten however, have chanced on, encouraged by way of gauge concept, absolutely new invariants. Strikingly, including the speculation defined during this ebook those invariants yield a wealth of latest effects concerning the differentiable constitution of algebraic surfaces. different advancements contain the systematic use of nef-divisors (in ac­ cordance with the growth made within the type of upper dimensional algebraic varieties), a greater realizing of Kahler constructions on surfaces, and Reider's new method of adjoint mappings. some of these advancements were included within the current version, although the Donaldson and Seiberg-Witten thought basically in terms of examples. in fact we use the chance to right a few minor errors, which we ether have stumbled on ourselves or which have been communicated to us by way of cautious readers to whom we're a lot obliged.

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