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Differential Topology of Complex Surfaces
Английски език
164 b
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120.16
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This book is about the smooth classification of a certain§class of algebraicsurfaces, namely regular elliptic§surfaces of geometric genus one, i.e. elliptic surfaces with§b1 = 0 and b2+ = 3. The authors give a complete§classification of these surfaces up to diffeomorphism. They§achieve this result by partially computing one of Donalson's§polynomial invariants. The computation is carried out using§techniques from algebraic geometry. In these computations§both thebasic facts about the Donaldson invariants and the§relationship of the moduli space of ASD connections with the§moduli space of stable bundles are assumed known. Some§familiarity with the basic facts of the theory of moduliof§sheaves and bundles on a surface is also assumed. This work§gives a good and fairly comprehensive indication of how the§methods of algebraic geometry can be used to compute§Donaldson invariants.
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Английски език
