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題名 離散型熱帶曲線因子秩之計算
Calculating Rank of Discrete Divisors on Tropical Curves
作者 張穎泓
貢獻者 蔡炎龍
張穎泓
關鍵詞 熱帶幾何
日期 2012
上傳時間 2-Sep-2013 16:46:53 (UTC+8)
摘要 本篇論文主要是在討論熱帶曲線上，離散型的因子應具備有哪些性質，而在討論
熱帶曲線上因子的性質時，我們會發現到致的計算，在低次熱帶曲線上，或是
因子本身的係數總和高時，並不是太困難。但再高次的熱帶曲線上，致的計算
就成線的極其繁雜，因此我們想要藉由在熱帶曲線上離散型的來幫助我們計算。
最後我們可以得到的結論是，若C是一平滑的熱帶曲線，則C上因子的致，
將會受到C的虧格所限制，大幅的簡化了我們在離散型熱帶曲線因子致的
計算。
參考文獻 Odagiri, Shinsuke , Tropical algebraic geometry ,Hokkaido Math. J. ,
F Hokkaido Mathematical Journal , 38 , 2009 , 4 , 771--795 , 0385-4035 ,Hannah Markwig ,

Baker, Matthew and Norine, Serguei , Riemann-{R och and {A bel-{J acobi theory on a finite graph , Adv. Math. ,F Advances in Mathematics , 215 , 2007 , 2 , 766--788 ,Tatiana Smirnova-Nagnibeda ,

Baker, Matthew , Specialization of linear systems from curves to graphs ,With an appendix by Brian Conrad , Algebra Number Theory ,F Algebra \\& Number Theory , 2 ,
2008 , 6 , 613--653 , 1937-0652 , 14C20 (05C99 14H51) ,

Gathmann, Andreas and Kerber, Michael ,R iemann-{R och theorem in tropical geometry ,
Math. Z. ,F Mathematische Zeitschrift , 259 ,
2008 , 1 , 217--230 ,0025-5874 , MAZEAX ,
14C40 (14H99 51M20) ,

Mikhalkin, Grigory and Zharkov, Ilia , Tropical curves, their {J acobians and theta functions ,BOOK Curves and abelian varieties ,

Voloshin, Vitaly I. , Introduction to graph theory ,PUBLISHER,Nova Science Publishers Inc. ,ADDRESS 2009 , 144


Mikhalkin, Grigory , Enumerative tropical algebraic geometry in, J. Amer. Math. Soc. ,F Journal of the American Mathematical Society , 18 , 2005 , 2 , 313--377 , 0894-0347 ,

Caporaso, Lucia and Harris, Joe , Counting plane curves of any genus , Invent. Math. ,F Inventiones Mathematicae , 131 , 1998 , 2 , 345--392 , 0020-9910 ,

Speyer, David and Sturmfels, Bernd , Tropical mathematics , Math. Mag. ,F Mathematics Magazine , 82 , 2009 , 3 , 163--173

Gao, S. and Lauder, A. G. B. , Decomposition of polytopes and polynomials , Discrete Comput. Geom. ,F Discrete \\& Computational Geometry. An International Journal,of Mathematics and Computer Science , 26 , 2001 , 1 , 89--104 , 0179-5376 , DCGEER ,

Fulton, William , Intersection theory ,SERIES ,Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in
Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics] ,2 ,EDITION = {Second ,PUBLISHER = {Springer-Verlag ,
ADDRESS = {Berlin , 1998 , xiv+470 ,ISBN = {3-540-62046-X; 0-387-98549-2 ,

Richter-Gebert, J{\\"u rgen and Sturmfels, Bernd and Theobald,
Thorsten , First steps in tropical geometry ,BOOK Idempotent mathematics and mathematical physics ,SERIES = {Contemp. Math. , 377 , 289--317 ,Amer. Math. Soc. ,{Providence, RI , 2005 , 14
描述 碩士
國立政治大學
應用數學研究所
100751001
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G1007510011
資料類型 thesis
dc.contributor.advisor 蔡炎龍zh_TW
dc.contributor.author (Authors) 張穎泓zh_TW
dc.creator (作者) 張穎泓zh_TW
dc.date (日期) 2012en_US
dc.date.accessioned 2-Sep-2013 16:46:53 (UTC+8)-
dc.date.available 2-Sep-2013 16:46:53 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2013 16:46:53 (UTC+8)-
dc.identifier (Other Identifiers) G1007510011en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/59437-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 100751001zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 本篇論文主要是在討論熱帶曲線上，離散型的因子應具備有哪些性質，而在討論
熱帶曲線上因子的性質時，我們會發現到致的計算，在低次熱帶曲線上，或是
因子本身的係數總和高時，並不是太困難。但再高次的熱帶曲線上，致的計算
就成線的極其繁雜，因此我們想要藉由在熱帶曲線上離散型的來幫助我們計算。
最後我們可以得到的結論是，若C是一平滑的熱帶曲線，則C上因子的致，
將會受到C的虧格所限制，大幅的簡化了我們在離散型熱帶曲線因子致的
計算。		zh_TW
dc.description.tableofcontents 書名頁................i
論文口試委員審定書......ii
授權書................iii
中文摘要..............iv
英文摘要..............v
誌謝.................vi
目錄.................vii
圖目錄................viii
第一章、緒論...........1
第二章、熱帶幾何........2
第三章、古典定理........11
第四章、圖形中的因子.....17
第五章、熱帶幾何上的因子..25		zh_TW
dc.format.extent 2407792 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1007510011en_US
dc.subject (關鍵詞) 熱帶幾何zh_TW
dc.title (題名) 離散型熱帶曲線因子秩之計算zh_TW
dc.title (題名) Calculating Rank of Discrete Divisors on Tropical Curvesen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Odagiri, Shinsuke , Tropical algebraic geometry ,Hokkaido Math. J. ,
F Hokkaido Mathematical Journal , 38 , 2009 , 4 , 771--795 , 0385-4035 ,Hannah Markwig ,

Baker, Matthew and Norine, Serguei , Riemann-{R och and {A bel-{J acobi theory on a finite graph , Adv. Math. ,F Advances in Mathematics , 215 , 2007 , 2 , 766--788 ,Tatiana Smirnova-Nagnibeda ,

Baker, Matthew , Specialization of linear systems from curves to graphs ,With an appendix by Brian Conrad , Algebra Number Theory ,F Algebra \\& Number Theory , 2 ,
2008 , 6 , 613--653 , 1937-0652 , 14C20 (05C99 14H51) ,

Gathmann, Andreas and Kerber, Michael ,R iemann-{R och theorem in tropical geometry ,
Math. Z. ,F Mathematische Zeitschrift , 259 ,
2008 , 1 , 217--230 ,0025-5874 , MAZEAX ,
14C40 (14H99 51M20) ,

Mikhalkin, Grigory and Zharkov, Ilia , Tropical curves, their {J acobians and theta functions ,BOOK Curves and abelian varieties ,

Voloshin, Vitaly I. , Introduction to graph theory ,PUBLISHER,Nova Science Publishers Inc. ,ADDRESS 2009 , 144


Mikhalkin, Grigory , Enumerative tropical algebraic geometry in, J. Amer. Math. Soc. ,F Journal of the American Mathematical Society , 18 , 2005 , 2 , 313--377 , 0894-0347 ,

Caporaso, Lucia and Harris, Joe , Counting plane curves of any genus , Invent. Math. ,F Inventiones Mathematicae , 131 , 1998 , 2 , 345--392 , 0020-9910 ,

Speyer, David and Sturmfels, Bernd , Tropical mathematics , Math. Mag. ,F Mathematics Magazine , 82 , 2009 , 3 , 163--173

Gao, S. and Lauder, A. G. B. , Decomposition of polytopes and polynomials , Discrete Comput. Geom. ,F Discrete \\& Computational Geometry. An International Journal,of Mathematics and Computer Science , 26 , 2001 , 1 , 89--104 , 0179-5376 , DCGEER ,

Fulton, William , Intersection theory ,SERIES ,Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in
Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics] ,2 ,EDITION = {Second ,PUBLISHER = {Springer-Verlag ,
ADDRESS = {Berlin , 1998 , xiv+470 ,ISBN = {3-540-62046-X; 0-387-98549-2 ,

Richter-Gebert, J{\\"u rgen and Sturmfels, Bernd and Theobald,
Thorsten , First steps in tropical geometry ,BOOK Idempotent mathematics and mathematical physics ,SERIES = {Contemp. Math. , 377 , 289--317 ,Amer. Math. Soc. ,{Providence, RI , 2005 , 14		zh_TW