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 thought of surfaces. the main sensational one matters the differentiable constitution of surfaces. two decades in the past little or no was once recognized approximately differentiable buildings on 4-manifolds, yet meanwhile Donaldson at the one hand and Seiberg and Witten however, have chanced on, encouraged by way of gauge conception, completely 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 knowing of Kahler buildings on surfaces, and Reider's new method of adjoint mappings. these kinds of advancements were included within the current version, even though the Donaldson and Seiberg-Witten thought basically in terms of examples. after all we use the chance to right a few minor blunders, which we ether have came upon ourselves or that have been communicated to us by way of cautious readers to whom we're a lot obliged.
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