Abstract
In the fundamental Sect. 1 we treat meromorphic maps induced by line bundles. Then, in Sect. 2, we deal with special features for differential forms on 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 non-algebraic surfaces. For instance, in Sect. 3 we give a direct proof (due to Lamari) that a compact surface is Kähler if and only if its first Betti number is even.
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© 2004 Springer-Verlag Berlin Heidelberg
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Barth, W.P., Hulek, K., Peters, C.A.M., Van de Ven, A. (2004). Some General Properties of Surfaces. In: Compact Complex Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57739-0_5
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DOI: https://doi.org/10.1007/978-3-642-57739-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00832-3
Online ISBN: 978-3-642-57739-0
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