## Kyoto Journal of Mathematics

### Automorphism groups of Joyce twistor spaces

Akira Fujiki

#### Abstract

We determine the automorphism groups of torus invariant self-dual structures defined by Joyce on the connected sum of copies of the complex projective plane. We determine, actually, the automorphism groups of the associated twistor spaces by using the results of our previous work. When the self-dual structures of Joyce and LeBrun coincide, our results recover the recent results of Honda and Viaclovsky on the automorphism groups of LeBrun’s self-dual structures.

#### Article information

Source
Kyoto J. Math., Volume 53, Number 2 (2013), 405-432.

Dates
First available in Project Euclid: 20 May 2013

https://projecteuclid.org/euclid.kjm/1369071234

Digital Object Identifier
doi:10.1215/21562261-2081252

Mathematical Reviews number (MathSciNet)
MR3079309

Zentralblatt MATH identifier
1284.53049

#### Citation

Fujiki, Akira. Automorphism groups of Joyce twistor spaces. Kyoto J. Math. 53 (2013), no. 2, 405--432. doi:10.1215/21562261-2081252. https://projecteuclid.org/euclid.kjm/1369071234

#### References

• [1] K. S. Brown, Cohomology of Groups, Grad. Texts in Math. 87, Springer, New York, 1982.
• [2] M. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), 417–445.
• [3] A. Fujiki, Compact self-dual manifolds with torus actions, J. Differential Geom. 55 (2000), 229–324.
• [4] P. S. Hilton and U. S. Stammbach, A Course in Homological Algebra, 2nd ed., Grad. Texts in Math. 4, Springer, New York, 1997.
• [5] N. Honda and J. Viaclovsky, Conformal symmetries of self-dual hyperbolic monopole metrics, Osaka J. Math. 50 (2013), 197–249.
• [6] D. Joyce, Explicit construction of self-dual 4-manifolds, Duke J. Math. 77 (1995), 519–552.
• [7] C. LeBrun, Explicit self-dual metrics on $\boldsymbol{C}\boldsymbol{P}^{2}\#\cdots\#\boldsymbol{C}\boldsymbol{P}^{2}$, J. Differential Geom. 34 (1991), 223–253.
• [8] T. Oda, Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties, Ergeb. Math. Grenzgeb. (3) 15, Springer, Berlin, 1988.
• [9] P. Orlik and F. Raymond, Actions of the torus on $4$-manifolds, I, Trans. Amer. Math. Soc. 152 (1970), 531–559.
• [10] H. Pedersen and Y. S. Poon, Equivariant connected sums of compact self-dual manifolds, Math. Ann. 301 (1995), 717–749.
• [11] Y. S. Poon, Compact self-dual manifolds with positive scalar curvature, J. Differential Geom. 24 (1986), 97–132.
• [12] Y. S. Poon, Conformal transformations of compact self-dual manifolds, Internat. J. Math. 5 (1994), 125–140.
• [13] R. Remmert and A. van de Ven, Zur Funktionentheorie homogener komplexer Mannigfaltigkeiten, Topology 2 (1963), 137–157.
• [14] J.-P. Serre, Corps locaux, Publ. Univ. Nancago 8, Hermann, Paris, 1968.