3 citations · 14 across the 14 of their papers we have counts for
14 papers
Applications of the Liouville symplectic form on the cotangent bundle of a loop group
Indranil Biswas, Michi-aki Inaba, Arata Komyo +2
Let be a semisimple, simply connected, affine algebraic group defined over . Consider the Liouville symplectic structure on the total space of the cotang…
Moduli spaces of framed logarithmic and parabolic connections on a Riemann surface
Indranil Biswas, Michi-aki Inaba, Arata Komyo +1
We construct moduli spaces of framed logarithmic connections and also moduli spaces of framed parabolic connections. It is shown that these moduli spaces possess a natural algebrai…
Canonical coordinates for moduli spaces of rank two irregular connections on curves
Arata Komyo, Frank Loray, Masa-Hiko Saito +1
In this paper, we study a geometric counterpart of the cyclic vector which allow us to put a rank 2 meromorphic connection on a curve into a ``companion'' normal form. This allow u…
A nonclassical algebraic solution of a 3-variable irregular Garnier system
Arata Komyo
In this paper, a nonclassical algebraic solution of a 3-variable irregular Garnier system is constructed. Diarra--Loray have studied classification of algebraic solutions of irregu…
Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification
Arata Komyo, Frank Loray, Masa-Hiko Saito
In this paper, we study rank 2 (quasi) parabolic bundles over the Riemann sphere with an effective divisor and these moduli spaces. First we consider a criterium when a parabolic b…
On the moduli spaces of framed logarithmic connections on a Riemann surface
Indranil Biswas, Michi-aki Inaba, Arata Komyo +1
We describe some results on moduli space of logarithmic connections equipped with framings on a -pointed compact Riemann surface.
Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities
Arata Komyo
In this paper, we consider the generalized isomonodromic deformations of rank two irregular connections on the Riemann sphere. We introduce Darboux coordinates on the parameter spa…
A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions
Arata Komyo
A. Girand has constructed an explicit two-parameter family of flat connections over the complex projective plane . These connections have dihedral monodromy and their…
The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations
Arata Komyo
In this paper, we study the moduli spaces of parabolic connections with a quadratic differential. We endow these moduli spaces with symplectic structures by using the fundamental 2…
Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections
Arata Komyo
In this paper, we treat moduli spaces of parabolic connections. We take étale coverings of the moduli spaces, and we construct a Hamiltonian structure of an algebraic vector field…
Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces
Arata Komyo, Masa-Hiko Saito
In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on and rank 2 (parabolic) Higgs bundle on $\mathbb{P…
On the types of the mixed Hodge structures of character varieties
Arata Komyo
In this paper, we show that the mixed Hodge structures of character varieties are of Hodge--Tate type and that the mixed Hodge polynomials are independent of the choice of generic…
Pure parts of the mixed Hodge structures of character varieties of indivisible type
Arata Komyo
We fix integers and . For a -punctured Riemann surface and a -tuple of partitions of , we can…
On compactifications of character varieties of -punctured projective line
Arata Komyo
In this paper, we construct compactifications of -character varieties of -punctured projective line and study the boundary divisor of the compactifications. Th…