arXiv subjects

Masaki Yoshino

Publications and source records attributed to Masaki Yoshino.

4 recordsLinked to original sources

arXiv2019

A Kobayashi-Hitchin correspondence between Dirac-type singular mini-holomorphic bundles and HE-monopoles

We prove an analogue of the Kobayashi-Hitchin correspondence oncompact connected 3-folds that is fibered on orbifold Riemann surfaces and satisfy an integrability condition, which contains compact connected Sasakian 3-folds. We define mini-holomorphic bundles on such 3-folds and the algebraic Dirac-type singularities on mini-holomorphic bundles, and prove that there exists a special Hermitian metric (admissible BHE-metric) on a Dirac-type singular mini-holomorphic bundle if the bundle satisfies a slope stability.

math.DG↗

arXiv2019

An $L^2$-index formula of monopoles with Dirac-type singularities

We prove the Fredholmness of Dirac operators of monopoles with Dirac-type singularities on oriented complete Riemannian $3$-folds, and we also calculate the $L^2$-indices of them.

math.DG↗

arXiv2018

The Nahm transform of spatially periodic instantons

We construct the Nahm transform from finite energy instantons on the product of a real line and a three dimensional torus to Dirac-type singular monopoles on the dual torus. Moreover, we show the correspondence between the data which handle the asymptotic behavior of instantons at infinity and one of monopoles at singular points.

math.DG↗

arXiv2017

Some characterizations of Dirac type singularity of monopoles

We study singular monopoles on open subsets in the $3$-dimensional Euclidean space. We give two characterizations of Dirac type singularities. One is given in terms of the growth order of the norms of sections which are invariant by the scattering map. The other is given in terms of the growth order of the norms of the Higgs fields.

math.DG↗