## On twistor spaces of anti-self-dual Hermitian surfaces

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- by Massimiliano Pontecorvo
- Trans. Amer. Math. Soc.
**331**(1992), 653-661 - DOI: https://doi.org/10.1090/S0002-9947-1992-1050087-0
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## Abstract:

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 $- \frac {1} {2}$ power of the canonical bundle of $Z$, if and only if there is a Kähler metric of zero scalar curvature in the conformal class of $h$. This has strong consequences on the geometry of $M$, which were also found by C. Boyer $[3]$ using completely different methods. We also prove the existence of a very close relation between holomorphic vector fields on $M$ and $Z$ in the case that $M$ is compact and Kähler.## References

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## Bibliographic Information

- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**331**(1992), 653-661 - MSC: Primary 32L25; Secondary 32J15, 32J17, 53C25, 53C55
- DOI: https://doi.org/10.1090/S0002-9947-1992-1050087-0
- MathSciNet review: 1050087