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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 inMathematics 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) 2012 en_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) G1007510011 en_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) 100751001 zh_TW dc.description (描述) 101 zh_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/#G1007510011 en_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 Curves en_US dc.type (資料類型) thesis en 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 inMathematics 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