Osaka Journal of Mathematics

New examples of compact minitwistor spaces and their moduli space

Nobuhiro Honda

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Abstract

In the paper [5] we obtained explicit examples of Moishezon twistor spaces of some compact self-dual four-manifolds admitting a non-trivial Killing field, and also determined their moduli space. In this note we investigate minitwistor spaces associated to these twistor spaces. We determine their structure, minitwistor lines and also their moduli space, by using a double covering structure of the twistor spaces. In particular, we find that these minitwistor spaces have different properties in many respects, compared to known examples of minitwistor spaces. Especially, we show that the moduli space of the minitwistor spaces is identified with the configuration space of different 4 points on a circle divided by the standard $\mathrm{PSL}(2,\mathbf{R})$-action.

Article information

Source
Osaka J. Math., Volume 47, Number 3 (2010), 717-730.

Dates
First available in Project Euclid: 24 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1285334472

Mathematical Reviews number (MathSciNet)
MR2768499

Zentralblatt MATH identifier
1203.32005

Subjects
Primary: 32L25: Twistor theory, double fibrations [See also 53C28] 32G05: Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15] 32G07: Deformations of special (e.g. CR) structures 53AA30 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Citation

Honda, Nobuhiro. New examples of compact minitwistor spaces and their moduli space. Osaka J. Math. 47 (2010), no. 3, 717--730. https://projecteuclid.org/euclid.ojm/1285334472


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