论文标题
抛物线希格斯束的模量在Riemann Sphere上的几何模型和权重变化：一个案例研究
Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
论文作者
论文摘要
我们构建了半稳定的模量空间的显式几何模型，在Riemann Sphere上强烈地抛物线Higgs束，在等级第二，四个标记点，任意程度和任意权重的情况下。构造机制依赖于基本的几何和组合技术，基于对某些精心制作的空间（一般非还原）捆绑捆绑式自动形态组的轨道稳定性的详细研究。上述技术并不是我们检查的案例的独特，这项工作阐明了一种通用方法，用于构建属0中半稳定抛物线式Higgs捆绑的任意模量空间，该空间被编码为重量多物质的组合。我们还对抛物线重量和墙壁变化的几何模型行为进行了全面分析，该行为集中在其nilpotent锥上。
We construct explicit geometric models for moduli spaces of semi-stable strongly parabolic Higgs bundles over the Riemann sphere, in the case of rank two, four marked points, arbitrary degree, and arbitrary weights. The mechanism of construction relies on elementary geometric and combinatorial techniques, based on a detailed study of orbit stability of (in general non-reductive) bundle automorphism groups on certain carefully crafted spaces. The aforementioned techniques are not exclusive to the case we examine, and this work elucidates a general approach to construct arbitrary moduli spaces of semi-stable parabolic Higgs bundles in genus 0, which is encoded into the combinatorics of weight polytopes. We also present a comprehensive analysis of the geometric models' behavior under variation of parabolic weights and wall-crossing, which is concentrated on their nilpotent cones.
