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Research Activity

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Field of Study

Algebraic Geometry

Subject of Study

Brill-Nöther theory (algebraic curve theory, Brill-Nöther theory, special linear system, Abelian variety, Jacobian variety) (I have been working on the field of Brill-Nöther theory and am producing many mathematical results with my collabolators. One is a generalization of Mumford-Martens theorem, i.e. a classification of a curve when dim W_d^r(C)=d-2r-2 and the other one is a generalization of G.Martens' theorem for odd-gonal curves. These two results are concerning about the structure of W_d^r(C), but unfortunately we use only an information of dimension of W_d^r(C). It seems that if we use more precise information about structure of W_d^r(C), we may get much results about an algebraic curve C. For this purpose, it is useful to determine a precise structure about W_d^r(C) i.e., the problems to determine a structure of W_d^r(C) forany (d,r) in case there is a special line bundle with degree d, dimension r (non-special case, this question is silly). If C is a double cover of a Brill-Nöther general curve E, this problem is studied by Ballico-Keem but it is not studied, yet in another case.)

Book / Paper

Book:

1. Akira Ohbuchi, Kazuhiro Konno, Noboru Nakayama, Atsushi Moriwaki and Usui Sampei :
Proceedings of the Symposium on Algebraic Geometry in East Asia,
World Scientific, Singapore, Jan. 2003.
2. Seiichi Wakaizumi, Akira Ohbuchi, Takuji Kawano, Takafumi Noma and Takao Hanabusa :
よりよい成績評価の仕方ハンドブック,
Center for University Extension, Tokushima, Dec. 2002.

Academic Paper (Judged Full Paper):

1. Akira Ohbuchi, Kei Miura and Takeshi Harui :
Automorphism group of plane curve computed by Galois points, II,
Proceedings of the Japan Academy. Series A, Mathematical Sciences, Vol.94, No.6, 59-63, 2018.
(Tokushima University Institutional Repository: 114266,   DOI: 10.3792/pjaa.94.59,   Elsevier: Scopus)
2. Akira Ohbuchi and Jiryo Komeda :
γ-Hyperelliptic Weierstrass Semigroups of Genus 6γ + 1 and 6γ,
Bulletin of the Brazilian Mathematical Society, Vol.48, No.2, 209-218, 2017.
(Tokushima University Institutional Repository: 114265,   DOI: 10.1007/s00574-016-0002-z,   Elsevier: Scopus)
3. Akira Ohbuchi and Kei Miura :
Automorphism group of plane curve computed by Galois points,
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol.56, No.2, 695-702, 2015.
(DOI: 10.1007/s13366-013-0181-3)
4. Akira Ohbuchi and Jiryo Komeda :
The Weierstrass Semigroups on Double Cver of genus Two Curves,
Tukuba Journal of Mathematics, Vol.38, No.2, 201-206, 2015.
5. Akira Ohbuchi and Takeshi Harui :
On the number of pencils of minimal degree on curves with small gonality,
JP Journal of Geometry and Topology, Vol.10, No.3, 191-229, 2011.
(Elsevier: Scopus)
6. Akira Ohbuchi, Kei Miura and Takeshi Takahashi :
Automorphisms of a nonsingular curve on a rational surface of Picard number three,
Far East Journal of Mathematical Sciences, Vol.47, No.1, 109-119, 2010.
(Elsevier: Scopus)
7. Akira Ohbuchi, Takeshi Harui and Takao Kato :
Quitient Curve of Smooth Plane Curves with Automorphism,
Kodai Mathematical Journal, Vol.33, No.1, 164-172, 2010.
(DOI: 10.2996/kmj/1270559164)
8. Akira Ohbuchi, Takeshi Harui and Takao Kato :
The minimal degree of plane models of algebraic curves and double coverings,
Geomertiae Dedicata, Vol.143, No.1, 181-192, 2009.
(DOI: 10.1007/s10711-009-9381-2)
9. Akira Ohbuchi and Takeshi Harui :
Double coverings between smooth plane curves,
Kodai Mathematical Journal, Vol.31, No.2, 257-262, 2008.
(DOI: 10.2996/kmj/1214442797,   CiNii: 130004687889)
10. Akira Ohbuchi and Jiryo Komeda :
Existence of the non-primitive Weierstrass gap sequences on curves of genus 8,
Bulletin of the Brazilian Mathematical Society, Vol.39, No.1, 109-121, 2008.
(DOI: 10.1007/s00574-008-0074-5)
11. Akira Ohbuchi and Changho Keem :
On the Castelnuovo-Severi inequality for a double covering,
Algebraic Geometry in East Asia II (Hanoi), No.1, 11-29, 2008.
12. Akira Ohbuchi and Jiryo Komeda :
On Double Covering of a Pointed non-singular Curve with any Wyerstrass Semigroup,
Tukuba Journal of Mathematics, Vol.30, No.1, 43-54, 2007.
13. Akira Ohbuchi and Jiryo Komeda :
Weierstrass Points with First Non-gap Four on a Double Covering of a Hyperelliptic Curve,
Serdica Mathematical Journal, Vol.30, No.1, 43-54, 2004.
14. Akira Ohbuchi, Takao Kato and Changho Keem :
On the variety Wdr(C) whose dimension is at least d-3r-2,
Journal of Pure and Applied Algebra, Vol.192, No.1-3, 159-172, 2004.
(DOI: 10.1016/j.jpaa.2004.01.006)
15. Akira Ohbuchi, Changho Keem and Kyung-Hye Cho :
Variety of net of degree g-1 on smooth algebraic curves of low genus,
Journal of Mathematical Society of Japan, Vol.55, No.3, 591-616, 2003.
(DOI: 10.2969/jmsj/1191418991,   Elsevier: Scopus)
16. Akira Ohbuchi, Changho Keem and Kyung-Hye Cho :
On the variety of special linear system of degree g-1 on smooth algebraic curves,
International Journal of Mathematics, Vol.13, No.1, 11-29, 2002.
17. Akira Ohbuchi, Masaaki Honma and Edoard Ballico :
On the order of speciality of a simple, special, and complete linear system on a curve,
Journal of the Korean Mathematical Society, Vol.39, No.4, 593-609, 2002.
(Elsevier: Scopus)
18. Akira Ohbuchi and Masaaki Honma :
Plane curves with aligned conductors,
Far East Journal of Mathematical Sciences, Vol.4, No.1, 21-53, 2002.
19. Akira Ohbuchi and Masaaki Honma :
A variant of a base-point-free pencil trick and linear systems on a plane curve,
Journal of the Korean Mathematical Society, Vol.36, No.3, 567-580, 2000.
(Elsevier: Scopus)
20. Akira Ohbuchi, Takao Kato and Changho Keem :
Normal generation of line bundles of high degrees on smooth algebraic curves,
Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg, Vol.69, 319-333, 2000.
(DOI: 10.1007/BF02940883,   Elsevier: Scopus)
21. Akira Ohbuchi, Edoardo Ballico, Changho Keem and Geriet Martens :
On curves of genus eight,
Mathematische Zeitschrift, Vol.227, 543-554, 1998.
22. Akira Ohbuchi, Takao Kato and Changho Keem :
Variety of special linear systems on k-sheeted coverings,
Geomertiae Dedicata, Vol.69, 53-65, 1998.
23. Akira Ohbuchi, Takao Kato and Changho Keem :
On triple coverings of irrational curves,
Tukuba Journal of Mathematics, Vol.21, No.2, 421-441, 1997.
24. Akira Ohbuchi :
On the difference of 4-gonal linear systems on some curves,
Serdica Mathematical Journal, Vol.23, 59-68, 1997.
25. Akira Ohbuchi :
On the construction of a special divisor of some special curve,
Natural Science Research, Faculty of Integrated Arts and Sciences, The University of Tokushima, Vol.29, 1-7, 1997.
(Tokushima University Institutional Repository: 108)
26. Akira Ohbuchi, Y Kashiwagi, I Kikumasa and O Miyagawa :
A note on equivalence and weight enumerators of codes,
Hiroshima Journal of Mathematical Education, Vol.4, 109-116, 1996.
27. Akira Ohbuchi :
On the heigher Wahl maps,
Tukuba Journal of Mathematics, Vol.18, No.1, 79-99, 1994.
28. Akira Ohbuchi :
A note on the normal generation of ample line bundles on an abelian surface,
Proceedings of the American Mathematical Society, Vol.117, No.1, 275-277, 1993.
29. Akira Ohbuchi and Takao Kato :
Very ampleness of multiple of tetragonal linear systems,
Communications in Algebra, Vol.21, No.12, 4587-4597, 1993.
30. Akira Ohbuchi :
On the projective normality of some varieties of degree 5,
Pacific Journal of Mathematics, Vol.144, No.2, 313-325, 1990.
31. Akira Ohbuchi :
A note on the projective normality of special line bundles on abelian varieties,
Tukuba Journal of Mathematics, Vol.12, No.2, 341-352, 1988.
32. Akira Ohbuchi :
A note on the normal generation of ample line bundles on abelian varieties,
Proceedings of the Japan Academy, Vol.64, No.4, 119-120, 1988.
33. Akira Ohbuchi :
Some criteria for reducible abelian varieties,
Tukuba Journal of Mathematics, Vol.12, No.2, 507-519, 1988.
34. Akira Ohbuchi :
Some remarks on ample line bundles on abelian verieties,
Manuscripta Mathematica, Vol.57, No.1, 225-238, 1987.

Academic Paper (Unrefereed Paper):

1. Akemi Yamano, Yoshifumi Nariyuki, Shogo Hirai and Akira Ohbuchi :
Problem Based Learning for the Career Education A Case of the Gender Equality and the Global Human Resources,
徳島大学大学教育研究ジャーナル, No.11, 51-64, 2014.
(Tokushima University Institutional Repository: 106327)
2. Akira Ohbuchi :
On Some Numerical Relations of -gonal Linear System,
Journal of Mathematics Tokushima University, Vol.31, 7-10, 1998.
(Tokushima University Institutional Repository: 121)
3. Akira Ohbuchi :
On the normal generation of ample line bundles on abelian varieties defined over some special field,
Journal of Mathematics Tokushima University, Vol.31, 7-10, 1997.
(Tokushima University Institutional Repository: 114)

Review, Commentary:

1. Akira Ohbuchi :
平面代数曲線,
数学セミナー, No.7, 30-35, Jul. 2004.

Proceeding of International Conference:

1. Hideji TANAKA, Yohei Kurokawa, Masaki Takeuchi and Akira Ohbuchi :
Amplitude modulated multiplexed flow analysis for simultaneous determination of multiple analytes. Determination of ferrous and ferric ions,
Flow Analysis Xll, Thessaloniki, Greece, Sep. 2012.
2. Akira Ohbuchi :
On the Variety Wdr(C) whose dimension is at least d-3r-2,
Proceedings of the International Conference held at Yamaguchi University, 87-102, Yamaguchi, Jan. 2003.
3. Akira Ohbuchi, Changho Keem and Kyung-Hye Cho :
Variety of special nets of degree g-1 on double coverings of a smooth plane quartic of genus 9,
Mathematical Journal, Vol.2, 971-984, Amsterdam, Oct. 2000.

Proceeding of Domestic Conference:

1. Atsushi Morishita, Akira Ohbuchi, Toshihiro Okamoto and Masanobu Haraguchi :
コホモロジーを用いた局在型表面プラズモンとドレスト光子の機能モデル,
第67回応用物理学会春季学術講演会, 15a-PA4-3, Mar. 2020.
2. Akira Ohbuchi :
Torres の定理の拡張について,
Aug. 2015.
3. Akira Ohbuchi :
平面代数曲線の自己同型について,
研究集会「代数曲線論」報告集, Aug. 2012.
4. Akira Ohbuchi :
クリフォード指数について,
研究集会「代数学シンポジューム」報告集, Aug. 2012.
5. Akira Ohbuchi :
二重被覆である曲線のワイアシュトラス点,
Sep. 2010.
6. 黒河 洋平, Masaki Takeuchi, Akira Ohbuchi and Hideji TANAKA :
振幅変調多重化フロー分析法の原理と応用. 塩化物イオン, 鉄イオンの定量,
日本分析化学会第59年会, Sep. 2010.
7. Akira Ohbuchi :
二重被覆面に於けるCastelnuovo-Severi不等式について,
「代数学シンポジウム」報告集, 17-26, Dec. 2003.
8. Akira Ohbuchi :
代数曲線とクリフォード指数について,
研究集会「リーマン面に関連する位相幾何学」報告集, 17-26, Oct. 2002.
9. Akira Ohbuchi :
On the Variety of Special Linear Systems of Degree g-1 on Smooth Algebraic Curves,
研究集会「1999代数幾何シンポジューム」報告集, 118-129, Apr. 2000.
10. Akira Ohbuchi :
代数曲線上の Special Linear System について,
研究集会「射影多様体/代数多様体の射影幾2+特異点」報告集, 82-89, May 1998.
11. Akira Ohbuchi :
代数曲線上の line bundle の normal generation について,
RIMS Kokyuroku, Vol.1065, 152-162, May 1998.
12. Akira Ohbuchi :
Pentagonal Curve の構成について,
RIMS Kokyuroku, Vol.1022, 58-70, May 1997.
13. Akira Ohbuchi :
Pentagonal Curve の構成,
「Hodge 理論と代数幾何」報告集, 106-120, Apr. 1996.
14. Akira Ohbuchi :
代数曲線上の Special Linear System について,
ワーク·ショップ「Hodge 理論·Log 幾何学·代数幾何学」報告集, 1-30, Apr. 1996.

Grants-in-Aid for Scientific Research (KAKEN Grants Database @ NII.ac.jp)

  • Research on Hurwitz's problem and K3 surfaces through double covers of curves and symmetric numerical semigroups (Project/Area Number: 15K04830 )
  • 代数曲線の自己同型群と射影モデル (Project/Area Number: 15K04822 )
  • Special linear systems and Weierstrass points on compact Riemann surfaces (Project/Area Number: 26400141 )
  • Development and application of Galois point theory of projective varieties (Project/Area Number: 26400057 )
  • Study on function fields of algebraic hypersurfaces focusing on projections, - for an evolution of Galois point theory - (Project/Area Number: 25400059 )
  • Studies of fibred complex surfaces from diversified perspectives (Project/Area Number: 24244002 )
  • Hurwitz' problem through double covers of curves and curves on surfaces (Project/Area Number: 24540057 )
  • Linear Systems on Algebraic Curves and its Applications (Project/Area Number: 24540042 )
  • Studies on special linear series and Weierstrass points on compact Riemann surfaces (Project/Area Number: 23540209 )
  • Hurwitz' problem on Weierstrass points on algebraic curves (Project/Area Number: 21540052 )
  • Linear Systems and Projective Models on Algebraic Curves (Project/Area Number: 21540043 )
  • Special linear systems on compact Riemann surfaces (Project/Area Number: 19540186 )
  • Linear Systems on Algebraic Curves and its Applications (Project/Area Number: 19540035 )
  • Special linear systems on Riemann surfaces (Project/Area Number: 17540160 )
  • Research on coverings of curves and toric varieties through Weierstrass points (Project/Area Number: 17540046 )
  • Algebraic Curves and its Applications (Project/Area Number: 17540030 )
  • Study on Galois embeddings of algebraic surfaces (Project/Area Number: 17540018 )
  • Special linear systems on compact Riemann surfaces (Project/Area Number: 15540173 )
  • Algebraic curves through commutative semigroups and its application to toric varieties (Project/Area Number: 15540051 )
  • Special Linear System on an Algebraic Curve and its Application (Project/Area Number: 15540035 )
  • Research on space curve and its Galois line (Project/Area Number: 15540016 )
  • Theory of algebraic curves with application toward the coding theory (Project/Area Number: 13640048 )
  • Special Linear Systems on Algebraic Curves (Project/Area Number: 13640029 )
  • Research on the structures of hypersurfaces and their function fields (Project/Area Number: 13640013 )
  • Meromorphic functions on compact Riemann surfaces (Project/Area Number: 12640180 )
  • Special Linear Linear Systems on Algebraic Curves (Project/Area Number: 11640032 )
  • Study of function fields with particular properties, and its application to coding theory (Project/Area Number: 10640048 )
  • Meromorphic functions on Riemann surfaces, Weierstrass points (Project/Area Number: 10440051 )
  • Study od Coding-Theory (Project/Area Number: 09640043 )
  • 類数問題とHomology代数的構造の研究 (Project/Area Number: 07640053 )
  • アーベル多様体の射影モデルの研究 (Project/Area Number: 06640056 )
  • On the Luroth semigroup of smooth Plane curves (Project/Area Number: 06044261 )
  • 正標数体上のTangencyとDuality (Project/Area Number: 05640046 )
  • 有限群のコホモロジー論の研究 (Project/Area Number: 04804002 )
  • 正標数体上の射影多様体のTangencyとDuality (Project/Area Number: 02804002 )
  • Search by Researcher Number (10211111)