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

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 techn...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2022
Автор: Meneses, Claudio
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2022
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211725
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study. Claudio Meneses. SIGMA 18 (2022), 062, 41 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Meneses, Claudio
author_facet Meneses, Claudio
citation_txt Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study. Claudio Meneses. SIGMA 18 (2022), 062, 41 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
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spelling Meneses, Claudio
2026-01-09T12:50:58Z
2022
Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study. Claudio Meneses. SIGMA 18 (2022), 062, 41 pages
1815-0659
2020 Mathematics Subject Classification: 14H60; 14D22; 32G13; 22E25
arXiv:2012.13389
https://nasplib.isofts.kiev.ua/handle/123456789/211725
https://doi.org/10.3842/SIGMA.2022.062
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.
I would like to thank Hartmut Weiß, whose encouragement and support were crucial in prompting the appearance of the present manuscript, Steven Rayan for providing many insightful remarks, and the anonymous referee for the careful revision of the manuscript and the constructive criticism provided. This work was supported by the DFG SPP 2026 priority programme “Geometry at infinity”.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
Article
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spellingShingle Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
Meneses, Claudio
title Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
title_full Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
title_fullStr Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
title_full_unstemmed Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
title_short Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
title_sort geometric models and variation of weights on moduli of parabolic higgs bundles over the riemann sphere: a case study
url https://nasplib.isofts.kiev.ua/handle/123456789/211725
work_keys_str_mv AT menesesclaudio geometricmodelsandvariationofweightsonmoduliofparabolichiggsbundlesovertheriemannsphereacasestudy