Titlebook: Compact Complex Surfaces; Wolf P. Barth,Klaus Hulek,Antonius Ven Book 2004Latest edition Springer-Verlag Berlin Heidelberg 2004

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0071-1136 ry 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 whom978-3-642-57738-3978-3-642-57739-0Series ISSN 0071-1136 Series E-ISSN 2197-5655

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Curves on Surfaces,ve on a surface and is treated in Sects. 1–6. The second theme, developed in Sects. 7–8 is embedded resolution of singularities of curves and the application to the so-called simple singularities of curves.

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Some General Properties of Surfaces,n compact surfaces. The main point is that for surfaces the Fröhlicher spectral sequence always degenerates. Combining the consequences of this fact with the topological index theorem we find, following Kodaira, relations between topological and analytical invariants which are crucial in handling no

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K3-Surfaces and Enriques Surfaces, main results in Sect. 2. In Chapt. IV, Sect. 3 we saw that K 3- surfaces are Kähler, a fact we use from the start. The main tool for studying moduli of K 3- surfaces is the period map and we describe these moduli spaces in terms of the corresponding period domains. This is done in Sect. 6–14 after