Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
TAKURO ABE Last modified date:2020.03.04

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

1. Takuro Abe, Alexandru Dimca, On complex supersolvable line arrangements, Journal of Algebra, 10.1016/j.jalgebra.2020.02.007, 552, 38-51, 2020.06.
2. 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].
3. 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..
4. 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。.
5. 阿部拓郎, Lukas Kühne, Heavy hyperplanes in multiarrangements and their freeness, Journal of Algebraic Combinatorics,, 48, 4, 581-606, 2018.12.
6. 阿部拓郎, Alexandru Dimca, Splitting types of bundles of logarithmic vector fields along plane curves, International Journal of Mathematics,, 29, 8, 1-20, 2018.10.
7. 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,, 493, 20-35, 2018.01.
8. 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,, 389-401, 2017.12.
9. 阿部 拓郎, Erratum to: Divisionally free arrangements of hyperplanes
, Inventiones Mathematicae,, 207, 3, 1377-1378, 2017.03.
10. 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.
11. 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.
12. 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.