Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study

Symmetry Integrability and Geometry-Methods and Applications

article

Claudio Meneses¹ 

[1] Mathematisches Seminar, Christian-Albrechts Universität zu Kiel

关键词: parabolic Higgs bundle;    Hitchin fibration;    nilpotent cone.;   

DOI  :  10.3842/SIGMA.2022.062

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown