hyperelliptic surface

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Enriques-Kodaira classification
In mathematics, the Enriques-Kodaira classification is a classification of compact complex surfaces. For complex projective surfaces it was done by Federigo Enriques, and Kunihiko Kodaira later extended it to non-algebraic compact surfaces. It has also been extended to surfaces in characteristic p > 0 by  Enrico Bombieri and David Mumford.
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