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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study
Claudio Meneses Mathematisches Seminar, Christian-Albrechts Universität zu Kiel, Heinrich-Hecht-Platz 6, 24118 Kiel, Germany
Аннотация:
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.
Ключевые слова:
parabolic Higgs bundle, Hitchin fibration, nilpotent cone.
Поступила: 21 сентября 2021 г.; в окончательном варианте 28 июля 2022 г.; опубликована 13 августа 2022 г.
Образец цитирования:
Claudio Meneses, “Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study”, SIGMA, 18 (2022), 062, 41 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1858 https://www.mathnet.ru/rus/sigma/v18/p62
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