Group actions on the tropical Hesse pencil

Atsushi Nobe

doi:10.1007/s13160-016-0226-8

Group actions on the tropical Hesse pencil

Atsushi Nobe^*

^*この研究の対応する著者

研究成果: Article › 査読

抄録

Addition of points on the tropical Hesse curve is realized via its intersections with two tropical lines. Then the addition formula for the points on the curve is reduced from the one for the level-three theta functions through the ultradiscretization procedure. In addition, a tropical analogue of the Hessian group G₂₁₆, the group of linear automorphisms acting on the Hesse pencil, is investigated; it is shown that the dihedral group D₃ of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.

本文言語	English
ページ（範囲）	537-556
ページ数	20
ジャーナル	Japan Journal of Industrial and Applied Mathematics
巻	33
号	3
DOI	https://doi.org/10.1007/s13160-016-0226-8
出版ステータス	Published - 2016 12月 1
外部発表	はい

ASJC Scopus subject areas

工学（全般）
応用数学

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10.1007/s13160-016-0226-8

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abstract = "Addition of points on the tropical Hesse curve is realized via its intersections with two tropical lines. Then the addition formula for the points on the curve is reduced from the one for the level-three theta functions through the ultradiscretization procedure. In addition, a tropical analogue of the Hessian group G216, the group of linear automorphisms acting on the Hesse pencil, is investigated; it is shown that the dihedral group D3 of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.",

keywords = "Hesse pencil, Hessian group, QRT system, Theta function, Tropical curve, Ultradiscretization",

author = "Atsushi Nobe",

note = "Funding Information: This work was partially supported by JSPS KAKENHI Grant Numbers 22740100 and 26400107. The author is grateful to an anonymous referee for his/her helpful comments and suggestions. Publisher Copyright: {\textcopyright} 2016, The JJIAM Publishing Committee and Springer Japan.",

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AU - Nobe, Atsushi

N1 - Funding Information: This work was partially supported by JSPS KAKENHI Grant Numbers 22740100 and 26400107. The author is grateful to an anonymous referee for his/her helpful comments and suggestions. Publisher Copyright: © 2016, The JJIAM Publishing Committee and Springer Japan.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Addition of points on the tropical Hesse curve is realized via its intersections with two tropical lines. Then the addition formula for the points on the curve is reduced from the one for the level-three theta functions through the ultradiscretization procedure. In addition, a tropical analogue of the Hessian group G216, the group of linear automorphisms acting on the Hesse pencil, is investigated; it is shown that the dihedral group D3 of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.

AB - Addition of points on the tropical Hesse curve is realized via its intersections with two tropical lines. Then the addition formula for the points on the curve is reduced from the one for the level-three theta functions through the ultradiscretization procedure. In addition, a tropical analogue of the Hessian group G216, the group of linear automorphisms acting on the Hesse pencil, is investigated; it is shown that the dihedral group D3 of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.

KW - Hesse pencil

KW - Hessian group

KW - QRT system

KW - Theta function

KW - Tropical curve

KW - Ultradiscretization

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Group actions on the tropical Hesse pencil

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