Arata Komyo
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
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Arata Komyo has a total of 3 co-authors. Here are the top co-authors by number of shared publications:
- Frank Loray
Univ Rennes CNRS IRMAR -UMR 6625 F-35000 Rennes France
1 shared publication - Masa-Hiko Saito
Department of Mathematics Kobe University 657-8501 Rokko Kobe Japan
1 shared publication - Masa-Hiko Saito1 shared publication
Latest Publications
- Open Access
Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification
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 bundle admits a unramified irregular singular parabolic connection. Second, to give a good compactification of the moduli space of semistable parabolic bundles, we introduce a generalization of parabolic bundles, which is called refined parabolic bundles. Third, we discuss a stability condition of refined parabolic bundles and define elementary transformations of the refined parabolic bundles. Finally, we describe the moduli spaces of refined parabolic bundles when the dimensions of the moduli spaces are two. These are related to geometry of some weak del Pezzo surfaces.
Open AccessModuli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification
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 bundle admits a unramified irregular singular parabolic connection. Second, to give a good compactification of the moduli space of semistable parabolic bundles, we introduce a generalization of parabolic bundles, which is called refined parabolic bundles. Third, we discuss a stability condition of refined parabolic bundles and define elementary transformations of the refined parabolic bundles. Finally, we describe the moduli spaces of refined parabolic bundles when the dimensions of the moduli spaces are two. These are related to geometry of some weak del Pezzo surfaces.
- Open Access
A nonclassical algebraic solution of a 3-variable irregular Garnier system
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 irregular Garnier systems. There are two type of the algebraic solutions: classical type and pull-back type. They have shown that there are exactly three nonclassical algebraic solutions for $N$-variables irregular Garnier systems with $N>1$. Explicit forms of two of the three solutions are already given. The solution constructed in the present paper is the remained algebraic solution.Open AccessA nonclassical algebraic solution of a 3-variable irregular Garnier system
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 irregular Garnier systems. There are two type of the algebraic solutions: classical type and pull-back type. They have shown that there are exactly three nonclassical algebraic solutions for $N$-variables irregular Garnier systems with $N>1$. Explicit forms of two of the three solutions are already given. The solution constructed in the present paper is the remained algebraic solution. - Open Access
Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities
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 space of a family of rank two irregular connections by apparent singularities. By the Darboux coordinates, we describe the generalized isomonodromic deformations as Hamiltonian systems.
Open AccessDescription of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities
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 space of a family of rank two irregular connections by apparent singularities. By the Darboux coordinates, we describe the generalized isomonodromic deformations as Hamiltonian systems.
- Open Access
- 26 October 2021
- Published by MathDoc/Centre Mersenne in Annales de la Faculté des sciences de Toulouse : Mathématiques
- Vol. 30 (3) , 479-501
A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions
A. Girand has constructed an explicit two-parameter family of flat connections over the complex projective plane . These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a conic and three tangent lines. In this paper, we give a generalization of this construction. That is, we construct an explicit -parameter family of flat connections over the complex projective space . Moreover, we discuss the relation between these connections and the Garnier system.- 26 October 2021
- Published by MathDoc/Centre Mersenne in Annales de la Faculté des sciences de Toulouse : Mathématiques
- Vol. 30 (3) , 479-501
Open AccessA family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions
A. Girand has constructed an explicit two-parameter family of flat connections over the complex projective plane . These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a conic and three tangent lines. In this paper, we give a generalization of this construction. That is, we construct an explicit -parameter family of flat connections over the complex projective space . Moreover, we discuss the relation between these connections and the Garnier system. - Open Access
Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections
In this paper, we treat moduli spaces of parabolic connections. We take \'etale coverings of the moduli spaces, and we construct a Hamiltonian structure of an algebraic vector field determined by the isomonodromic deformation for each \'etale morphism.
Open AccessHamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections
In this paper, we treat moduli spaces of parabolic connections. We take \'etale coverings of the moduli spaces, and we construct a Hamiltonian structure of an algebraic vector field determined by the isomonodromic deformation for each \'etale morphism.
- Open Access
Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces
In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on $\mathbb{P}^1$ and rank 2 (parabolic) Higgs bundle on $\mathbb{P}^1$. Then we obtain explicit descriptions of Zariski open sets of the moduli space of the parabolic connections and the moduli space of the Higgs bundles. For $n=5$, we can give global descriptions of the moduli spaces in detail.Open AccessExplicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces
In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on $\mathbb{P}^1$ and rank 2 (parabolic) Higgs bundle on $\mathbb{P}^1$. Then we obtain explicit descriptions of Zariski open sets of the moduli space of the parabolic connections and the moduli space of the Higgs bundles. For $n=5$, we can give global descriptions of the moduli spaces in detail. - 11 October 2016
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 225, 185-206
MIXED HODGE STRUCTURES OF THE MODULI SPACES OF PARABOLIC CONNECTIONS
In this paper, we investigate the mixed Hodge structures of the moduli space of -stable parabolic Higgs bundles and the moduli space of -stable regular singular parabolic connections. We show that the mixed Hodge polynomials are independent of the choice of generic eigenvalues and the mixed Hodge structures of these moduli spaces are pure. Moreover, by the Riemann–Hilbert correspondence, the Poincaré polynomials of character varieties are independent of the choice of generic eigenvalues.
- 11 October 2016
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 225, 185-206
MIXED HODGE STRUCTURES OF THE MODULI SPACES OF PARABOLIC CONNECTIONS
In this paper, we investigate the mixed Hodge structures of the moduli space of -stable parabolic Higgs bundles and the moduli space of -stable regular singular parabolic connections. We show that the mixed Hodge polynomials are independent of the choice of generic eigenvalues and the mixed Hodge structures of these moduli spaces are pure. Moreover, by the Riemann–Hilbert correspondence, the Poincaré polynomials of character varieties are independent of the choice of generic eigenvalues.
- 10 December 2015
- Published by Springer Nature in manuscripta mathematica
- Vol. 150 (3-4) , 441-464
An explicit description of the relative ${SL_{4}(\mathbb{C})}$ S L 4 ( C ) -character variety of the projective line- 10 December 2015
- Published by Springer Nature in manuscripta mathematica
- Vol. 150 (3-4) , 441-464
An explicit description of the relative ${SL_{4}(\mathbb{C})}$ S L 4 ( C ) -character variety of the projective line- Open Access
On compactifications of character varieties of $n$-punctured projective line
In this paper, we construct compactifications of $SL_2(\mathbb{C})$-character varieties of $n$-punctured projective line and study the boundary divisor of the compactifications. This study is motivated by the conjecture for the configuration of the boundary divisor, due to C. Simpson. We verify the conjecture for a few examples.
Open AccessOn compactifications of character varieties of $n$-punctured projective line
In this paper, we construct compactifications of $SL_2(\mathbb{C})$-character varieties of $n$-punctured projective line and study the boundary divisor of the compactifications. This study is motivated by the conjecture for the configuration of the boundary divisor, due to C. Simpson. We verify the conjecture for a few examples.