Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
TAKURO ABE Last modified date:2021.10.12

Professor / Division of Fundamental mathematics / Institute of Mathematics for Industry


Papers
1. 阿部拓郎, Roots of the characteristic polynomials of hyperplane arrangements and their restrictions and localizations, Topology and its Applications (special volume), to appear, 2021.10.
2. Takuro Abe;Alexandru Dimca;Gabriel Sticlaru, Addition-deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements , Journal of Algebraic Combinatorics , https://doi.org/10.1007/s10801-020-00986-9, 2020.11.
3. 阿部拓郎、寺尾宏明、Tan Nhat Tran, On A_1^2 restrictions of Weyl arrangements, Journal of Algebraic Combinatorics, https://doi.org/10.1007/s10801-020-00979-8, 54, 1 , 353-379, 2020年9月にオンライン上で公開。2021年8月に冊子体で出版。, 2020.09.
4. 阿部拓郎、中島規博, A Characterization of High Order Freeness for Product Arrangements and Answers to Holm’s Questions, Algebras and Representation Theory, https://doi.org/10.1007/s10468-020-09961-1, 24, 585-599, 2021.06.
5. 阿部拓郎, Double Points of Free Projective Line Arrangements, International Mathematics Research Notices, https://doi.org/10.1093/imrn/rnaa145, 現在オンライン版のみ, 2020.06, 射影平面中の超可解配置の二重点の数に関するDirac-Motzkin予想であるAnzis–Tohăneanu予想を、対数的ベクトル場の自由性という代数を用いて解決することに成功した。論文は受理済みで、冊子媒体はまだだが、電子媒体で公開されている。.
6. 阿部拓郎, Plus-one Generated and Next to Free Arrangements of Hyperplanes, INTERNATIONAL MATHEMATICS RESEARCH NOTICES, https://doi.org/10.1093/imrn/rnz099, 2021, 12, 9233-9261, オンライン公開は2019年6月。, 2021.06, We introduce a new class of arrangements of hyperplanes, called (strictly) plus-one generated arrangements, from algebraic point of view. Plus-one generatedness is close to freeness, that is, plus-one generated arrangements have their logarithmic derivation modules generated by dimension plus-one elements, with relations containing one linear form coefficient. We show that strictly plus-one generated arrangements can be obtained if we delete a hyperplane from free arrangements. We show a relative freeness criterion in terms of plus-one generatedness. In particular, for plane arrangements, we show that a free arrangement is in fact surrounded by free or strictly plus-one generated arrangements. We also give several applications..
7. 阿部拓郎、堀口達也、枡田幹也、村井聡、佐藤敬志, Hessenberg varieties and hyperplane arrangements, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, https://doi.org/10.1515/crelle-2018-0039, 764, 241-286, 2020.07, 半単純複素線型代数群とそれに対応するルートポセットのイデアル、及び作用素から定まるHessenberg多様体と、ルートポセットのイデアルから定まるイデアル配置を考える。
本論文では、一見全く関係がないこの二つの対象に対し、前者の作用素が正則冪零である場合のコホモロジー環と、後者の対数的ベクトル場から定まるアルチン環が同型であるという全く新しく強力な関係性を見出した。これは正則冪零の場合のベッチ数、及びコホモロジー環の表示、正則半単純作用素のワイル群作用不変部分の決定とHessenberg多様体の完全交差性・ホッジ・リーマン関係式やレフシェッツ性、更にPetersonがアナウンスした結果への肯定的解答、更にSommers-Tymoczkoの第一予想の解決など、数多の関連結果を持つ。.
8. Takuro Abe, Alexandru Dimca, On complex supersolvable line arrangements, Journal of Algebra, 10.1016/j.jalgebra.2020.02.007, 552, 38-51, 2020.06.
9. Takuro Abe, Toshiaki Maeno, Satoshi Murai and Yasuhide Numata, Solomon-Terao algebra of hyperplane arrangements
, Journal of the Matiemathcal Society of Japan, 71, 4, 1027-1047, 2019.10, [URL].
10. Takuro Abe, Hiroaki Terao, Multiple addition, deletion and restriction theorems for hyperplane arrangements, Proceedings of the American Mathematical Society, 10.1090/proc/14592, 147, 11, 4835-4845, 2019.11, In the study of free arrangements, the most useful result to construct/ check free arrangements is the addition-deletion theorem in [J. Fac. Sci. Univ. Tokyo 27 (1980), 293-320]. Recently, the multiple version of the addition theorem was proved in [J. Eur. Math. Soc. 18 (2016), 1339-1348], called the multiple addition theorem (MAT), to prove the ideal-free theorem. The aim of this article is to give the deletion version of MAT, the multiple deletion theorem (MDT). Also, we can generalize MAT to get MAT2 from the viewpoint of our new proof. Moreover, we introduce the restriction version, a multiple restriction theorem (MRT). Applications of MAT2, including the combinatorial freeness of the extended Catalan arrangements, are given..
11. 阿部拓郎, Deletion theorem and combinatorics of hyperplane arrangements, Mathematische Annalen, 10.1007/s00208-018-1713-9, 373, 1-2, 581-595, 2019.02, [URL], 自由配置から一枚超平面を抜いたものが再び自由になるかを判定する寺尾の除去定理の成立条件が完全に組み合わせ論で記述されることを示した。.
12. 阿部拓郎, Lukas Kühne, Heavy hyperplanes in multiarrangements and their freeness, Journal of Algebraic Combinatorics, https://doi.org/10.1007/s10801-017-0806-y, 48, 4, 581-606, 2018.12.
13. 阿部拓郎, Alexandru Dimca, Splitting types of bundles of logarithmic vector fields along plane curves, International Journal of Mathematics, https://doi.org/10.1142/S0129167X18500556, 29, 8, 1-20, 2018.10.
14. 阿部 拓郎, 陶山大輔, A basis construction of the extended Catalan and Shi arrangements of the type A2, Journal of Algebra, doi.org/10.1016/j.jalgebra.2017.09.024, 493, 20-35, 2018.01.
15. 阿部拓郎, Restrictions of free arrangements and the division theorem, Proceedings of the Intensive Period "Perspectives in Lie Theory", Springer INdAM Series ; 19, https://doi.org/10.1007/978-3-319-58971-8_14, 389-401, 2017.12.
16. 阿部 拓郎, Erratum to: Divisionally free arrangements of hyperplanes
, Inventiones Mathematicae, https://doi.org/10.1007/s00222-016-0714-0, 207, 3, 1377-1378, 2017.03.
17. 阿部 拓郎, 陶山大輔, 辻栄周平, The freeness of Ish arrangements, Journal of Combinatorial Theory Series A, 146, 169-183, 2017.02.
18. 阿部 拓郎, Daniele Faenzi, Jean Valles, Logarithmic bundles of deformed Weyl arrangements of type A_2, Bulletin de la Societe Mathematique de France, 144, 4, 745-761, 2016.12.
19. 阿部 拓郎, Chambers of 2-affine arrangements and freeness of 3-arrangements, Journal of Algebraic Combinatorics, 10.1007/s10801-012-0393-x, 38, 1, 65-78, 2013.08.