悬链奇点的极小解图的构造与周期性
Construction and Periodicity of Minimal Resolution Graphs of Suspension Singularities
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中文总结 AI 辅助
本文开发了构造悬链奇点极小解图的计算工具，含Magma与SageMath程序，证明三类悬链奇点的极小解图具周期性，还提供了生成紧致化解图及检查图同构的程序。
中文摘要 AI 辅助
我们开发了用于构造悬链奇点极小解图的计算工具。具体而言，我们提供了一个Magma程序，该程序实现了Nemethi算法，可用于构造任意悬链奇点的极小解图，该程序以结构化图数据形式输出所得解图，编码了图的顶点、边和装饰。我们还开发了一个SageMath程序，以该数据为输入生成解图的图形表示，便于其可视化与分析。针对三类悬链奇点族，我们证明了相应的极小解图是周期性的，周期等于对应单值化因子分解的阶数。我们还提供了用于生成悬链奇点的紧致化解图以及在指定参数范围内检查图同构的Magma程序。
英文摘要
We develop computational tools for constructing the minimal resolution graphs of suspension singularities. In particular, we provide a Magma program that implements Nemethi's algorithm that can be used to construct the minimal resolution graph of any suspension singularity. The program outputs the resulting resolution graph as structured graph data, encoding the vertices, edges, and decorations of the graph. We further develop a SageMath program that takes this data as input and produces graphical representations of the resolution graphs, facilitating their visualization and analysis. For three families of suspension singularities, we prove that the corresponding minimal resolution graphs are periodic, with periods equal to the orders of the corresponding monodromy factorizations. We also provide Magma programs for generating compactified resolution graphs of suspension singularities and checking graph isomorphisms over a specified range of parameters.
