Directory of Researchers

KOMYO Arata
Center for Mathematical and Data Sciences
Associate Professor
Mathematics
Last Updated :2022/05/14

Researcher Profile and Settings

Affiliation

  • <Faculty / Graduate School / Others>

    Center for Mathematical and Data Sciences

Teaching

Research Activities

Research Areas

  • Natural sciences / Algebra

Published Papers

  • On the moduli spaces of framed logarithmic connections on a Riemann surface

    I. Biswas, M.-A. Inaba, A. Komyo, M.-H. Saito

    2021, Comptes Rendus Mathématique, 359 (5), 617 - 624

    [Refereed]

  • A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions

    Arata Komyo

    2021, Annales de la Faculté des Sciences de Toulouse, 6 (30), 479 - 501

    [Refereed]

  • Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections

    Arata Komyo

    2022, Journal of the Mathematical Society of Japan, 74 (2), 473 - 519

    [Refereed]

  • Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces

    Arata Komyo, Masa-Hiko Saito

    2019, Kyoto Journal of Mathematics, 59 (3), 515 - 552

    [Refereed]

  • The moduli spaces of parabolic connections with a quadratic differential and isomonodromic deformations

    Arata Komyo

    2018, SIGMA, 14 (111)

    [Refereed]

  • Arata Komyo

    In this paper, we investigate the mixed Hodge structures of the moduli space of alpha-stable parabolic Higgs bundles and the moduli space of a-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 Poincare polynomials of character varieties are independent of the choice of generic eigenvalues.

    CAMBRIDGE UNIV PRESS, Mar. 2017, Nagoya Mathematical Journal, 225, 185 - 206, English

    [Refereed]

    Scientific journal

  • Arata Komyo

    In this paper, we give an explicit description of a certain character variety of dimension 2, and we construct a compactification of the character variety. We show that the compactification is a del Pezzo surface. One motivation of the explicit description is investigation of the mixed Hodge structure of the character variety. For the character variety, we can verify some conjectures on the mixed Hodge structures and the configurations of the boundaries of compactifications.

    SPRINGER HEIDELBERG, Jul. 2016, Manuscripta Mathematica, 150 (3-4), 441 - 464, English

    [Refereed]

    Scientific journal

  • On compactifications of character varieties of n-pointed projective line

    Arata Komyo

    In this paper, we construct compactifications of SL2 (C)-character varieties of n-punctured projective line and study the boundary divisors of the compactifications. This study is motivated by a conjecture for the configurations of the boundary divisors, due to C. Simpson. We verify the conjecture for a few examples.

    ANNALES INST FOURIER, 2015, Annales de l'institut Fourier, 65 (4), 1493 - 1523, English

    [Refereed]

    Scientific journal

MISC

  • Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities

    Arata Komyo

    2020, arXiv:2003.08045

  • On compactifications of character varieties and a conjecture of Simpson

    KOMYO Arata

    2012, 射影多様体の幾何とその周辺2012報告集

  • Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification

    Arata Komyo, Frank Loray, Masa-Hiko Saito

    Mar. 2022, arXiv:2203.10816

Presentations

  • Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification

    KOMYO, Arata

    Algebraic Geometry and Integrable Systems 2022, 10 Feb. 2022, English

    [Invited]

    Invited oral presentation

  • Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities

    Komyo, Arata

    Indo-Japan Web-Workshop on Vector Bundles and Related Topics (zoom), 24 Feb. 2021, English

    [Invited]

    Invited oral presentation

  • Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities

    KOMYO Arata

    Kobe Seminar on Integrable Systems (zoom), 27 May 2020, Japanese

    [Invited]

    Invited oral presentation

  • Dihedral monodromy を持つ射影空間上の平坦接続の族と Garnier 系の代数解

    光明 新

    湯布院代数幾何学ワークショップ (日本文理大学), 29 Dec. 2019

    [Invited]

  • Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections

    KOMYO Arata

    Mini Workshop on Geometry of Moduli Spaces (Kobe University), 09 Oct. 2019

    [Invited]

  • A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions

    KOMYO Arata

    Journée Paris-Rennes du GDR EFI (L'Institut Henri Poincaré), 28 Aug. 2019, English

    [Invited]

  • Dihedral monodromy を持つ射影空間上の平坦接続の族と Garnier 系の代数解

    光明 新

    アクセサリー・パラメーター研究会 (熊本大学), 15 Mar. 2019

  • The moduli spaces of parabolic connections with a quadratic differential and isomonodromic deformations

    KOMYO Arata

    Conformal field theory, isomonodromy tau-functions and Painlevé equations, 2018 (Kobe University), 12 Dec. 2018

    [Invited]

  • The moduli spaces of parabolic connections with a quadratic differential and isomonodromic deformations

    KOMYO Arata

    Algebraic Geometry Seminar (Kyoto University), 16 Nov. 2018

    [Invited]

  • A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions

    KOMYO Arata

    Séminare de Géométrie analytique (Université de Rennes 1), 27 Sep. 2018

    [Invited]

  • Dihedral monodromy を持つ射影空間上の平坦接続の族と Garnier 系の代数解

    光明 新

    ホッジ理論と代数幾何学 (東京電機大学), 23 Aug. 2018

    [Invited]

  • The moduli spaces of parabolic connections with a quadratic differential and isomonodromic deformations

    光明 新

    Workshop on Accessory Parameters (東京大学玉原国際セミナーハウス), 07 Oct. 2017

  • Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections

    KOMYO Arata

    Algebraic Geometry and Integrable Systems, Kobe 2016 (Kobe University), 08 Dec. 2016

    [Invited]

  • Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections

    光明 新

    Workshop on accessory parameters (東京大学玉原国際セミナーハウス), 24 Aug. 2016

  • Geometric description of the moduli space of parabolic connections on $\mathbb{P}^1\setminus \{t_1,...,t_5\}$ and the universal family

    光明 新

    アクセサリー・パラメーター研究会, 熊本大学, 22 Mar. 2016

  • Geometric description of the moduli space of parabolic connections on $\mathbb{P}^1\setminus \{t_1,...,t_5\}$ and the universal family

    KOMYO Arata

    Kobe-Lyon Summer School in mathematics 2015 (Kobe University), 30 Jul. 2015

    [Invited]

  • On the mixed Hodge structures of the moduli spaces of connections

    KOMYO Arata

    The 10th Kagoshima Algebra--Analysis--Geometry Seminar, 16 Feb. 2015

    [Invited]

  • On the types of the mixed Hodge structures of character varieties, Kobe-Leuven workshop on Geometry and Integrable Systems

    KOMYO Arata

    Kobe-Leuven Workshop on Geometry and Integrable Systems (KU Leuven), 08 Jul. 2014

    [Invited]

  • On the types of the mixed Hodge structures of character varieties, Kobe-Leuven workshop on Geometry and Integrable Systems

    KOMYO Arata

    Workshop Moduli spaces of connections (Universite de Rennes 1), 03 Jul. 2014

    [Invited]

  • Character varietyの混合Hodge構造について

    光明 新

    超幾何方程式研究会2014 (神戸大学), 05 Jan. 2014

  • On compactifcations of character varieties of $n$-punctured projective line

    KOMYO Arata

    Moduli theory in Algebraic geometry and Integrable systems (RIMS), 20 Sep. 2013

    [Invited]

  • Character Varietyに関するSimpson予想とP=W予想

    光明 新

    代数多様体のトポロジーとその周辺 (北海道大学), 22 Aug. 2013

    [Invited]

  • ある種のcharacter varietyのコンパクト化とSimpson予想

    光明 新

    アクセサリー・パラメーター研究会 (熊本大学), 16 Mar. 2013

  • On compactifications of character varieties and a conjecture of Simpson

    光明 新

    第 11 回アフィン代数幾何学研究集会 (関西学院大学), 02 Mar. 2013

    [Invited]

  • ある種のcharacter varietyのコンパクト化とSimpson予想

    光明 新

    超幾何方程式研究会2013 (神戸大学), 05 Jan. 2013

  • On compactifications of character varieties and a conjecture of Simpson

    光明 新

    射影多様体の幾何とその周辺 2012 (高知大学), 06 Oct. 2012

    [Invited]

  • Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification

    Komyo, Arata

    Web-seminar on Painlevé Equations and related topics, 06 May 2022, English

    [Invited]

Association Memberships

  • THE MATHEMATICAL SOCIETY OF JAPAN

Research Projects

  • モノドロミー保存変形を記述する微分方程式の代数解の研究

    光明 新

    独立行政法人日本学術振興会, 科学研究費助成事業/若手研究, Apr. 2019 - Mar. 2023, Principal investigator

    Competitive research funding