Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/63704
題名: 搬硬幣遊戲與離散型熱帶因子等價關係
The Chip-Firing Game and Equivalence of Discrete Tropical Divisors
作者: 王珮紋
Wang, Pei Wen
貢獻者: 蔡炎龍
Tsai, Yen Lung
王珮紋
Wang, Pei Wen
關鍵詞: 熱帶曲線
因子
tropical curve
divisor
chip-firing game
日期: 2013
上傳時間: 10-二月-2014
摘要: 在這篇論文裡,我們研究Baker-Norine的搬硬幣遊戲,並且把這個遊戲應用在離散型的熱帶因子上。特別地,我們去探討這個遊戲與等價熱帶因子之間的關係。最後我們證明了下面的定理:若$D, E$為熱帶曲線$\\Gamma$上的離散型熱帶因子, 而$\\overline{D}$, $\\overline{E}$分別代表因子$D,E$在搬硬幣遊戲時的狀態,因子$D$與$E$等價,若且為若 $\\overline{D}$可經搬硬幣遊戲變成$\\overline{E}$。
In this thesis, we study Baker-Norine`s chip-firing game, and apply it to discrete tropical divisors. In particularly, we discuss the relationship between this game and the equivalence of divisors.\n\n Finally, we give a proof of the theorem: \nLet $D$ and $E$ be discrete tropical divisors of tropical curve $\\Gamma$, and let $\\overline{D}$ and $\\overline{E}$ be corresponding configurations of the chip-firing game. \nThe divisors $D$ and $E$ are equivalent if and only if $\\overline{D}$ can be transformed into $\\overline{E}$.
參考文獻: [1] Matthew Baker. Specialization of linear systems from curves to graphs. Algebra\nNumber Theory, 2(6):613–653, 2008. With an appendix by Brian Conrad.\n[2] Matthew Baker and Serguei Norine. Riemann-Roch and Abel-Jacobi theory\non a finite graph. Adv. Math., 215(2):766–788, 2007.\n[3] N. L. Biggs. Chip-firing and the critical group of a graph. J. Algebraic Combin.,\n9(1):25–45, 1999.\n[4] Anders Björner, László Lovász, and Peter W. Shor. Chip-firing games on\ngraphs. European J. Combin., 12(4):283–291, 1991.\n[5] Andreas Gathmann and Michael Kerber. A Riemann-Roch theorem in tropical\ngeometry. Math. Z., 259(1):217–230, 2008.\n[6] Christian Haase, Gregg Musiker, and Josephine Yu. Linear systems on tropical\ncurves. Math. Z., 270(3-4):1111–1140, 2012.\n[7] Shinsuke Odagiri. Tropical algebraic geometry. Hokkaido Math. J.,\n38(4):771–795, 2009.\n[8] Jürgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps\nin tropical geometry. In Idempotent mathematics and mathematical physics,\nvolume 377 of Contemp. Math., pages 289–317. Amer. Math. Soc., Providence,\nRI, 2005.\n[9] David Speyer and Bernd Sturmfels. Tropical mathematics. Math. Mag.,\n82(3):163–173, 2009.\n[10] Yen-Lung Tsai. Working with tropical meromorphic functions of one variable.\nTaiwanese J. Math., 16(2):691–712, 2012.
描述: 碩士
國立政治大學
應用數學系數學教學碩士在職專班
100972008
102
資料來源: http://thesis.lib.nccu.edu.tw/record/#G0100972008
資料類型: thesis
Appears in Collections:學位論文

Files in This Item:
File SizeFormat
200801.pdf1.23 MBAdobe PDF2View/Open
Show full item record

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.