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Hermitian surfaces and a twistor space of algebraic dimension $ 2$

Author: Massimiliano Pontecorvo
Journal: Proc. Amer. Math. Soc. 113 (1991), 177-186
MSC: Primary 32J20; Secondary 32J17, 32L25, 53C55
MathSciNet review: 1074754
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Abstract: We study anti-self-dual hermitian surfaces with odd first Betti number. We show that the twistor space of a Hopf surface $ M$ has algebraic dimension 2, and we prove existence of half-conformally-flat metrics on the connected sum of copies of $ M$ and $ \mathbb{C}{\mathbb{P}_2}$. Finally we emphasize some differences with the case $ {b_1}$ even.

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