熱帶曲線上因子之秩的計算

Abstract

本計畫的目標是實際計算給定熱帶曲線因子的秩。目前已有不少熱帶版的 黎曼-羅赫定理的研究, 這自然是我們的重要工具之一。更重要的是, 我們創 造了一個有希望簡化計算的技巧, 並且應用 Baker-Norine, Amini-Caporaso, Hladký-Král’-Norine 的理論完成我們的目標。最後我們會撰寫一個計算熱帶 因子的套件, 協助本項及日後其他相關研究工作進行。

In this project, we would like to carry out explicitly calculation of the rank of divisors of a tropical curve. We do have the Riemann-Roch for tropical curves which is of course an important tool for us. Moreover, we take a brand new approach to do the task, which will simplify the computation. We will also study and apply techniques provided by Baker-Norine, Amini- Caporaso, and Hladký-Král’-Norine to help our calculation. Finally, we will develop a computer package to deal with divisors of tropical curves.