发表机构
Univ Montpellier, CNRS（蒙彼利埃大学，法国国家科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过符号-数值框架搜索Delzant八边形的相对K-不稳定性，发现数值上看似不稳定的构型经精确重构后均被消除，并解释了Wang-Zhou构造无法给出显式例子的原因。
AI 中文摘要
环簇的相对K-稳定性可以通过显式的Donaldson-Futaki计算来检验，然而寻找不稳定例子仍然具有挑战性。我们开发了一个可复现的符号-数值框架，用于研究对应于Picard秩为六的光滑环面的全部十五族Delzant八边形。虽然数值优化识别出若干看似不稳定的构型，但精确的有理数重构系统地消除了所观察到的不稳定性。我们解释了为何Wang和Zhou在2014年关于相对K-不稳定八边形的初步构造无法提供显式例子。
英文摘要
Relative K-stability of toric varieties can be tested through explicit Donaldson-Futaki computations, yet finding unstable examples remains challenging. We develop a reproducible symbolic-numeric framework to investigate all fifteen families of Delzant octagons corresponding to smooth toric surfaces of Picard rank six. While numerical optimization identifies several apparently destabilizing configurations, exact rational reconstruction systematically removes the observed instability. We explain why Wang and Zhou's 2014 tentative construction of a relatively K-unstable octagon does not allow to find an explicit example.
Comments18 pages. This work originated from a series of discussions between a pure mathematician and a physicist with a background in numerical methods
