Twistor spaces with meromorphic functions

Poon, Y. S.

doi:10.1090/S0002-9939-1991-1036990-0

Twistor spaces with meromorphic functions
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Proc. Amer. Math. Soc. 111 (1991), 331-338 Request permission

Abstract:

Among the class of Kähler surfaces with zero scalar curvature, only the twistor space of those surfaces which are also Ricci-flat can admit nonconstant meromorphic functions. Moreover, the transcendental degree of the function field of the twistor space over such surfaces is equal to one. This result leads to a classification of twistor spaces with positive algebraic dimensions.

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