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In mathematics, an Enoki surface is compact complex surface with positive second Betti number that has a global spherical shell and a non-trivial divisor D with H0(O(D)) ≠ 0 and (D, D) = 0. Enoki (1980) constructed some examples. They are surfaces of class VII, so are non-Kähler and have Kodaira dimension −∞.

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Enoki, Ichiro (1980), "On surfaces of class VII0 with curves", Japan Academy. Proceedings. Series A. Mathematical Sciences 56 (6): 275–279, doi:10.3792/pjaa.56.275, ISSN 0386-2194, MR 581470

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