arXiv subjects

Takashi Ono

Publications and source records attributed to Takashi Ono.

8 recordsLinked to original sources

arXiv2026

Manton's Exotic Vortex Equation

In this paper, we study the equation which we call Manton's exotic vortex equation. The equation arose in Manton's study of a deformation of the classical vortex equation [Ma]. We first investigate the existence problem for Manton's exotic vortex equation and establish existence results. We then construct the moduli space of solutions. Finally, we establish a dimensional reduction for Manton's exotic vortex equation. More precisely, we establish a correspondence between solutions of Manton's exotic vortex equation and pseudo-Hermitian-Yang--Mills connections with pseudo-Hermitian metrics of signature (1,1).

math.DG↗

arXiv2026

Moduli Spaces of the Basic Hitchin Equation on Sasakian Threefolds

In this paper, we study an equation which we call the basic Hitchin equation. This is an equation defined on Sasakian threefolds and is a three-dimensional analog of the Hitchin equation, which is defined on Riemann surfaces. We construct the moduli space of the basic Hitchin equation and show that such a space admits a hyperKähler metric. This also shows that the moduli space of flat bundles over Sasakian threefolds admits a hyperKähler metric. We also calculate the dimension of the moduli space.

math.DG↗

arXiv2026

Notes on acceptable bundles I

The notion of acceptable bundles plays a fundamental role in the Simpson--Mochizuki theory. This paper presents a detailed study of acceptable bundles on a punctured disk. In addition to its expository aspects, we introduce a new invariant and provide arguments that differ from those of Simpson and Mochizuki.

math.AG↗

arXiv2026

Notes on acceptable bundles II

The notion of acceptable bundles plays a fundamental role in the Simpson--Mochizuki theory. We study acceptable bundles on a partially punctured polydisk in detail. While this article is primarily expository, it also presents new arguments that differ from those of Mochizuki.

math.AG↗

arXiv2025

Dimensional reduction of stable Higgs bundle and the Doubly-Coupled Vortex Equations

Let $X$ be a compact Riemann surface and $\mathbb{P}^1$ be the complex projective line. In this paper, we introduce an equation which we call the doubly-coupled vortex equation on $X$. We show that the existence of a solution of the doubly-coupled is equivalent to the existence of an $SU(2)$-invariant Hermitian-Einstein metric on certain Higgs bundles over $X\times \mathbb{P}^1$. By applying the Kobayashi-Hitchin correspondence for Higgs bundles, we further show that the existence of a solution to the doubly-coupled vortex equation is equivalent to the stability of the associated Higgs quadruplet.

math.DG↗

arXiv2024

Harmonic Bundles with Symplectic Structures

We study harmonic bundles with an additional structure called symplectic structure. We study them for the case of the base manifold is compact and non-compact. For the compact case, we show that a harmonic bundle with a symplectic structure is equivalent to principle $Sp(2n,C)$-bundle with a reductive flat connection. For the non-compact case, we show that a polystable good filtered Higgs bundle with a perfect skew-symmetric pairing is equivalent to a good wild harmonic bundle with a symplectic structure.

math.AG↗

arXiv2023

Structure of the Kuranishi Spaces of pairs of Kähler manifolds and Polystable Higgs bundles

Let $X$ be a compact Kähler manifold and $(E,\overline\partial_E,θ)$ be a Higgs bundle over it. We study the structure of the Kuranishi space for the pair $(X, E,θ)$ when the Higgs bundle admits a harmonic metric or equivalently when the Higgs bundle is polystable and the Chern classes are 0. Under such assumptions, we show that the Kuranishi space of the pair $(X,E,θ)$ is isomorphic to the direct product of the Kuranishi space of $(E,θ)$ and the Kuranishi space of $X$. Moreover, when $X$ is a Riemann surface and $(E,\overline\partial_E,θ)$ is stable and the degree is 0, we show that the deformation of the pair $(X,E,θ)$ is unobstructed and calculate the dimension of the Kuranishi space.

math.AG↗

arXiv2022

Deformations of holomorphic-Higgs pairs

We study the deformation of the holomorphic-Higgs pair. The holomorphic-Higgs pair is a pair of a complex manifold and a Higgs bundle over it. We introduce the differential graded Lie algebra (DGLA) which comes from the deformation. We derive the Maurer-Cartan equation which governs the deformation of the holomorphic-Higgs pair, construct the Kuranishi family of it, and prove its local completeness.

math.DG↗