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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	537-556
Number of pages	20
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/s13160-016-0226-8
Publication status	Published - 2016 Dec 1
Externally published	Yes

Keywords

Hesse pencil
Hessian group
QRT system
Theta function
Tropical curve
Ultradiscretization

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

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10.1007/s13160-016-0226-8

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title = "Group actions on the tropical Hesse pencil",

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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language = "English",

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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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DO - 10.1007/s13160-016-0226-8

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EP - 556

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

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ER -

Group actions on the tropical Hesse pencil

Abstract

Keywords

ASJC Scopus subject areas

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