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On twistor spaces of anti-self-dual Hermitian surfaces

On twistor spaces of anti-self-dual Hermitian surfaces

We consider a complex surface M with anti-self-dual hermitian metric h and study the holomorphic properties of its twistor space Z .We show that the naturally defined divisor line bundle [X] is isomorphic to the -j power of the canonical bundle of Z , if and only if there is …