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Abstract

A universally known and in many ways most basic compact complex surface is the projective plane. Some obvious questions concerning ℙ2 have fascinated many a geometer, in particular the question (raised by Severi in [Sev]) whether a surface which is homeomorphic to ℙ2, is also isomorphic to ℙ2. The last and very difficult step towards the affirmative answer was done only in the late 1970s by S. - T. Yau. The striking point is that the only known proof uses analysis (hidden in Riemann-Roch for non-algebraic surfaces) and differential geometry as well as the methods of analytic and algebraic geometry.

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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). Examples. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-57739-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00832-3

  • Online ISBN: 978-3-642-57739-0

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