High Quality Content by WIKIPEDIA articles! In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality between Chern numbers of compact complex surfaces of general type. Its major interest is the way it restricts the possible topological types of the underlying real 4-manifold. It was proved independently by S.-T. Yau (1977, 1978) and Yoichi Miyaoka (1977), after Van de Ven (1966) and Fedor Bogomolov (1978) proved weaker versions with the constant 3 replaced by 8 and 4. Borel and Hirzebruch showed that the inequality is best possible by finding infinitely many cases where equality holds. The inequality is false in positive characteristic: (Lang 1983) and Easton (2008) gave examples of surfaces in characteristic p, such as generalized Raynaud surfaces, for which it fails.

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