Nobuhiro Honda

Double solid twistor spaces: the case of arbitrary signature

In a recent paper ([9]) we constructed a series of new Moishezon twistor spaces which are a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on nCP2 for arbitrary n≥3, which can be regarded as a generalization of the twistor spaces of ‘double solid type’ on 3CP2 studied by Kreußler, Kurke, Poon and the author. Similarly to the twistor spaces of ‘double solid type’ on 3CP2, projective models of the present twistor spaces have a natural structure of double covering of a CP2-bundle over CP1. We explicitly give a defining polynomial of the branch divisor of the double covering, whose restriction to fibers is degree four. If n≥4 these are new twistor spaces, to the best of the author’s knowledge. We also compute the dimension of the moduli space of these twistor spaces. Differently from [9], the present investigation is based on analysis of pluri-(half-)anticanonical systems of the twistor spaces.

Conformal symmetries of self-dual hyperbolic monopole metrics

We determine the group of conformal automorphisms of the self-dual metrics on n#CP due to LeBrun for n ≥ 3, and Poon for n = 2. These metrics arise from an ansatz involving a circle bundle over hyperbolic three-space H3 minus a finite number of points, called monopole points. We show that for n ≥ 3 connected sums, any conformal automorphism is a lift of an isometry of H3 which preserves the set of monopole points. Furthermore, we prove that for n = 2, such lifts form a subgroup of index 2 in the full automorphism group, which we show is a semi-direct product (U(1)×U(1))⋉D4, the dihedral group of order 8.

A new series of compact minitwistor spaces and Moishezon twistor spaces over them

Abstract In recent papers [Honda, J. Diff. Geom 82: 411–444, 2009], [Honda, Invent. Math 174, 463–504, 2008], we gave explicit description of some new Moishezon twistor spaces. In this paper, developing the method in the papers much further, we explicitly give projective models of a number of new Moishezon twistor spaces, as conic bundles over some rational surfaces (called minitwistor spaces). These include the twistor spaces studied in the papers as very special cases.

On a construction of the twistor spaces of Joyce metrics

In 1995 D. Joyce explicitly constructed a series of self-dual metrics with torus action on the connected sums of complex projective planes. In this paper we explicitly construct the twistor spaces of some of Joyces self-dual metrics. Starting from a fiber space whose fibers are compact singular toric surfaces, we apply a number of birational transformations to obtain the required twistor spaces. In the construction an important role is played by flops, a useful operation in algebraic geometry.

Donaldson-Friedman construction and deformations of a triple of compact complex spaces

Let Z be a three-dimensional complex manifold and M a (real) oriented fourmanifold. Z is said to be a twistor space of M if there exist a C°°-map π : Z —> M and a fixed point free anti-holomorphic involution σ : Z —> Z such that the following conditions are fulfilled: (1) π gives Z a C°° S-bundle structure over M. The fiber Lp := π~ (p) for any p e M is a complex submanifold of Z (which is biholomorphic to the complex projective line P 1 ) , (2) σ preserves each Lp and the automorphism on M induced by σ is the identity, (3) for any p G M, NLP/Z (= the holomorphic normal bundle of Lp in Z) is isomorphic to 0(1)® , where 0(1) denotes the line bundle of degree one over Lp. π is called the twistor fibration, σ the real structure and Lp a twistor line. A complex subspace X on Z is said to be real if σ(X) = X. A fundamental theorem of Penroses twistor theory is that there exists a natural one to one correspondence between twistor spaces Z of M and self-dual conformal structures [g] on M [2].

Equivariant deformations of meromorphic actions on compact complex manifolds

Abstract. Meromorphicity is the most basic property for holomorphic

Degenerations of LeBrun Twistor Spaces

{\mathbb C}^*

On pluri-half-anticanonical systems of LeBrun twistor spaces

-actions on compact complex manifolds. We prove that the meromorphicity of

Equivariant deformations of LeBrun’s self-dual metrics with torus action

{\mathbb C}^*

Toric LeBrun metrics and Joyce metrics

-actions on compact complex manifolds are not necessarily preserved by small deformations, if the complex dimension of complex manifolds is greater than two. In contrast, we also show that the meromorphicity of