论文标题
Riemann-Roch用于感谢您的曲折等级功能
Riemann-Roch for Toric Rank Functions
论文作者
论文摘要
在这篇论文中，我们研究了芯片射击游戏的曲折等级功能，并证明了猜想的Riemann-Roch的特殊情况。对这一研究领域进行调查的最初动机是为了通过使用芯片发射游戏改编（由于马特·贝克（Matt Baker））将Riemann-Roch改编为理论模拟。在这里，我们收集已知的结果，并提出了指示Riemann的新观察结果 - Roch持有树木和多边形。我们还证明了Riemann-Roch（即〜riemann-roch）的渐近案例。最后，我们还提供了岩浆代码和计算证据，Riemann-Roch为感谢您提供的曲线级功能。
In this thesis we study toric rank functions for chip firing games and prove special cases of a conjectural Riemann-Roch. The original motivation for an investigation into this area of study came for the adaptation (due to Matt Baker) of Riemann-Roch into a graph theoretic analogue through the use of chip-firing games. Here, we collect known results and present new observations that indicate Riemann--Roch holds for trees and polygons. We also prove an asymptotic case of Riemann--Roch (i.e.~Riemann--Roch for divisors of large degree). Finally, we also provide magma code and computational evidence that Riemann--Roch holds for the toric rank function.
