論文リスト

論文（掲載済みまたはアクセプト済み）：

1. The stability of the family of A_2-type arrangements, T. Abe, Journal of Mathematics of Kyoto University, Vol. 46 (2006), no. 3, pp617--636.

2. The elementary transformation of vector bundles on regular schemes, T. Abe,  Transactions of the American Mathematical Society, Vol. 359 (2007), no. 9, pp4285--4295.

3. The characteristic polynomial of a multiarrangement, T. Abe, H. Terao and M. Wakefield, Advances in Mathematics, Vol. 215 (2007), pp825--838.

4. Free and non-free multiplicity on the deleted $A_3$ arrangement, T. Abe, Proceedings of the Japan Academy, Series A, Vol. 83 (2007), no. 7, pp99--103.

5. Splitting criterion for reflexive sheaves, T. Abe and M. Yoshinaga, Proceedings of the American Mathematical Society, Vol. 136 (2008), no. 6, pp1887--1891. 

6. The Euler multiplicity and addition-deletion theorems for multiarrangements,  T. Abe, H. Terao and M. Wakefield, Journal of the London Mathematical Society, Vol. 77 (2008), no. 2, pp335--348.

7. Signed-eliminable graphs and free multiplicities on the braid arrangement, T. Abe, K. Nuida and Y. Numata, Journal of the London Mathematical Society,  Vol. 80 (2009), no. 1, pp121--134. 

8. Coxeter multiarrangements with quasi-constant multiplicities, T. Abe and M. Yoshinaga, Journal of Algebra, Vol. 322 (2009), no. 8, pp2839--2847. 

9. The stability of the family of B_2-type arrangements, T. Abe, Communications in Algebra, Vol. 37 (2009), no. 4, pp1193--1215. 

10. Totally free arrangements of hyperplanes, T. Abe, H. Terao and M. Yoshinaga,  Proceedings of the American Mathematical Society, Vol. 137 (2009), no. 4, pp1405--1410.

11. A primitive derivation and logarithmic differential forms of Coxeter arrangements, T. Abe and H. Terao, Mathematische Zeitschrift, Vol. 264 (2010), no. 4, pp 813--828. 

12. The freeness of Shi-Catalan arrangements, T. Abe and H. Terao, European Journal of Combinatorics, Vol. 32 (2011), pp1191--1198.

13. Primitive filtrations of the modules of invariant logarithmic forms of Coxeter arrangements, T. Abe and H. Terao, Journal of Algebra, Vol. 330 (2011), pp 251-262.

14. Exponents of 2-multiarrangements and multiplicity lattices, T. Abe and Y. Numata, Journal of Algebraic Combinatorics, Vol. 35, no. 1 (2012), pp1--17.

15. On the conjecture of Athanasiadis related to freeness of a family of hyperplane arrangements, T. Abe, Mathematical Research Letters, Vol. 19, no. 2 (2012), pp469--474.

16. Equivariant multiplicities of Coxeter arrangements and invariant bases, T. Abe, H. Terao and A. Wakamiko, Advances in Mathematics, Vol. 230 (2012), pp2364--2377. 

17. Characteristic polynomials, $\eta$-complexes and freeness of tame arrangements, T. Abe, Michigan Mathematical Journal, Vol. 62, no. 1 (2013), pp117--130.

18. Chambers of 2-affine arrangements and freeness of 3-arrangements, T. Abe, Journal of Algebraic Combinatorics, Vol. 38, no. 1 (2013), 65--78.

19. Free arrangements and coefficients of characteristic polynomials, T. Abe and M. Yoshinaga, Mathematische Zeitschrift, Vol. 275, no. 3 (2013), 911--919.

20. Roots of characteristic polynomials and intersection points of line arrangements, T. Abe,  Journal of Singularities, Vol.8 (2014), 100-117. 

21. Simple-root bases for Shi arrangements, T. Abe and H. Terao, Journal of Algebra, Vol. 422 (2015), 89--104. 

22. A mathematical problem for security analysis of hash functions and pseudorandom generators, K. Nuida, T. Abe,  S. Kaji, T. Maeno and Y. Numata, International Journal of Foundations of Computer Science, Vol. 26 (2015), No. 2, 169--194.

23. The freeness of ideal-Shi arrangements and free paths in affine Weyl arrangements, T. Abe and H. Terao, Journal of Algebraic Combinatorics, Vol. 43 (2016), Issue 1, 33--44.

24. Divisionally free arrangemetns of hyperplanes, T. Abe, Inventiones Mathematicae, Vol. 204 (2016), no. 1, 317--346.

25. Non-recursive freeness and non-rigidity of plane arrangements, T. Abe, M. Cuntz, H. Kawanoue and T. Nozawa, Discrete Mathematics, Vol. 339 (2016), Issue 5, 1430--1449.

26. The freeness of ideal subarrangements of Weyl arrangements, T. Abe, M. Barakat, M. Cuntz, T. Hoge and H. Terao,  Journal of the European Mathematical Society, Vol. 18 (2016). no. 6, 1339--1348.

27. Logarithmic bundles of deformed Weyl arrangements of type A_2, T. Abe, D. Faenzi and J. Valles, Bulletin de la Soci\'{e}t\'{e} Math\'{e}matique de France, Vol. 144 (2016), no. 4, 745--761. 

28. The freeness of Ish arrangements, T. Abe, D. Suyama and S. Tsujie, Journal of Combinatorial Theory Series A, Vol. 146 (2017), 169--183.

29. Erratum to: Divisionally free arrangements of hyperplanes, T. Abe , Inventiones Mathematicae, Vol. 207 (2017), no. 3, 1377--1378. 

30. Restrictions of free arrangements and the division theorem, T. Abe, Proceedings of the Intensive Period "Perspectives in Lie Theory", Springer INdAM Series ; 19 (2017), 389--401.

31. A basis construction of the extended Catalan and Shi arrangements of the type A_2, T. Abe and D. Suyama, Journal of Algebra, Vol. 493 (2018), 20--35. 

32. Heavy hyperplanes in multiarrangements and their freeness, T. Abe and L. Kuehne, Journal of Algebraic Combinatorics, Vol. 48 (2018), no.4, 581--606.

33. Splitting types of bundles of logarithmic vector fields along plane curves, T. Abe and A. Dimca, International Journal of Mathematics, Vol. 29 (2018), no. 8.

34. Deletion theorem and combinatorics of hyperplane arrangements, T. Abe,  Mathematische Annalen, Vol. 373 (2019), no. 1-2, 581–595.

35. Hessenberg varieties and hyperplane arrangements, T. Abe, T. Horiguchi, M. Masuda, S. Murai and T. Sato, Journal für die reine und angewandte Mathematik,  Vol. 764 (2020), 241--286.

36. Multiple addition, deletion and restriction theorems for hyperplane arrangements, T. Abe and H. Terao,  Proceedings of the American Mathematical Society,  Vol. 147 (2019),  no. 11,  4835–4845.

37.  Solomon-Terao algebra of hyperplane arrangements, T. Abe, T. Maeno, S. Murai and Y. Numata, Journal of the Mathematical Society of Japan, Vol. 71 (2019), no. 4, 1027-1047.

38.  Plus-one generated and next to free arrangements of hyperplanes, T. Abe, International Mathematical Research Notices, Vol. 2021 (2021), no. 12, 9233 --9261.

39. On complex supersolvable line arrangements, T. Abe and A. Dimca,  Journal of Algebra, Vol. 552 (2020), 38–51.

40. A Characterization of High Order Freeness for Product Arrangements and Answers to Holm’s Questions, T. Abe and N. Nakashima, Algebras and Representation Theory 24 (2021), no. 3, 585--599.

41. Double points of free projective line arrangements , T. Abe, International Mathematical Research Notices, to appear. arXiv:1911.10754 (2019).

42. On A_1^2 restrictions of Weyl arrangements, T. Abe, H. Terao and T. Nhat Tran, Journal of Algebraic Combinatorics 54 (2021), No.1, 353--379.

43. Addition-deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements , T. Abe, A. Dimca and G. Sticlaru,  Journal of Algebraic Combinatorics 54 (2021), No.3, 739--766.

44. Locally heavy hyperplanes in multiarrangements , T. Abe and L. Kuehne, Journal of Pure and Applied Algebra 226(1), 14pp.

45. Roots of the characteristic polynomials of hyperplane arrangements and their restrictions and localizations, T. Abe,  Topology and its Applications 313 (2022), Paper No. 107990, 13pp.

46. On some freeness-type properties for line arrangements, T. Abe, D. Ibadula and A. Măcinic, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 25 (2024), issue 1, 427--447.

47.  Addition-deletion theorem for free hyperplane arrangements and combinatorics. T. Abe, Journal of Algebra 610 (2022), 1--17.

48. Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one, T. Abe, Algebraic Combinatorics, accepted.  arXiv:2206.15059 (2022)

49. Addition-deletion theorems for the Solomon-Terao polynomials and B-sequences of hyperplane arrangements.  T. Abe, Mathematische Zeitschrift 306 (2024), no. 2, 25. 

50. Vertex-weighted digraphs and freeness of arrangements between Shi and Ish, T. Abe, T. N. Tran and S. Tsujie,  European Journal of Combinatorics 118 (2024), 103920.

51. A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups, T. Abe, G. Roehrle, C. Stump and M. Yoshinaga, Journal of Combinatorial Algebra, accepted. arxiv:1809.05026 (2018).

52.  Projective dimensions of hyperplane arrangements, T. Abe, Transactions of the American Mathematical Society, accepted. arXiv:2009.04101 (2020)

プレプリント：

1. Free reflection multiarrangements and quasi-invariants, T. Abe, N. Enomoto, M. Feigin and M. Yoshinaga, arXiv:2112.06738 (2021)

2. Deletion-Restriction for Logarithmic Forms on Multiarrangements, T. Abe and G. Denham, arXiv:2203.04816 (2022)

3. Free paths of arrangements of hyperplanes, T. Abe and T. Yamaguchi, arXiv:2306.11310 (2023)

4. Projective dimension of weakly chordal graphic arrangements. T. Abe. L. Kuehne, P.  Muecksch and L. Muehlherr, arXiv:2307.06021 (2023)

5. On Ziegler's conjectures for logarithmic derivations of arrangements, T. Abe and G. Denham, arXiv:2307.08173  (2023)

6.  Worpitzky-compatible sets and the freeness of arrangements between Shi and Catalan, T. Abe and T. Nhat Tran, arxiv:240317274

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