Abe Hiraku

アベヒラク | Abe Hiraku

Affiliation and department：

Research field (1)： Geometry

Research keywords (7)： Hessenberg varieties , Transformation groups , Schubert calculus , Toric varieties , Algebraic geometry , Algebraic topology , Combinatorics

Research theme for competitive and other funds (8)：

2023 - 2028 ヘッセンバーグ多様体とトーリック幾何の繋がり
2022 - 2023 Hessenberg多様体の幾何学と組み合わせ論
2020 - 2022 Hessenberg多様体のトポロジーと組合せ論
2018 - 2022 ヘッセンバーグ多様体の族と可積分系
2019 - 2020 トーラス群作用の幾何とトポロジー

Show all

Papers (17)：

Hiraku Abe, Haozhi Zeng. Totally nonnegative part of the Peterson variety in Lie type A. Math. Z. 2025. 309. 71
Hiraku Abe, Erik Insko. On singularity and normality of regular nilpotent Hessenberg varieties. J. Algebra. 2024. 651. 70-110
Hiraku Abe, Tatsuya Horiguchi, Hideya Kuwata, Haozhi Zeng. Geometry of Peterson Schubert calculus in type A and left-right diagrams. Algebr. Comb. 2024. 7. 2. 383-412
Hiraku Abe, Naoki Fujita, Haozhi Zeng. Fano and Weak Fano Hessenberg Varieties. Michigan Math. J. 2023. 73. 3. 511-555
Hiraku Abe, Tatsuya Horiguchi. A survey of recent developments on Hessenberg varieties. Schubert calculus and its applications in combinatorics and representation theory. 2020. 251-279

ｍore...

MISC (7)：

Hiraku Abe, Haozhi Zeng. Peterson varieties and toric orbifolds associated to Cartan matrices. 2023
阿部拓. A型Peterson Schubert calculusの幾何と計算. 数理解析研究所講究録. 2022. 2231. 54-59
Hiraku Abe, Haozhi Zeng. The integral cohomology rings of Peterson varieties in type A. arXiv:2203.02629. 2022
阿部拓. 旗多様体上のあるベクトル束に現れる正則Poisson構造と完全可積分系について. 数理解析研究所講究録. 2018. 2098. 76-82
阿部拓. ルート系から定まるトーリック多様体上の交叉数とヤング図 (変換群の位相幾何と代数構造). 数理解析研究所講究録. 2014. 1922. 78-83

ｍore...

Books (1)：

トゥー多様体
裳華房 2019 ISBN:9784785315863

Lectures and oral presentations (80)：

On Peterson isomorphism and toric geometry
(Workshop on Hessenberg varieties, Lusztig varieties, and Affine Grassmannians (IBS) 2025)
Divisors on regular Hessenberg varieties for h=(2, 3, 4, ..., n, n)
(The 7th Korea Toric Topology Workshop (KAIST) 2025)
Peterson varieties and toric geometry
(Superspace coinvariants, hyperplane arrangements and Hessenberg varieties (Waseda University) 2024)
Peterson variety and toric geometry
(Workshop on toric topology 2024 in Shanghai (online) 2024)
Peterson variety とトーリック幾何
(AGU 表現論セミナー表現論のランドスケープ (青山学院大学) 2024)

ｍore...

Association Membership(s) (1)：

THE MATHEMATICAL SOCIETY OF JAPAN

※ Researcher’s information displayed in J-GLOBAL is based on the information registered in researchmap. For details, see here.

Return to Previous Page