Asymptotic geometry of the Higgs bundle moduli space

希格斯丛模空间的渐近几何

• 批准号: 339380321
• 负责人: Professor Dr. Hartmut Weiß, since 4/2021
• 金额: --
• 依托单位: Mathematisches Seminar
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/339380321?language=en
• 关键词: Asymptotic; geometry; Higgs; bundle; moduli

Subject of this proposal are moduli spaces of Higgs bundles and their asymptotic geometry. Here we intend to come to a better understanding of the recent compactification by singular solutions of Hitchin's self-duality equations in the case of solutions which belong to holomorphic quadratic differentials with multiple zeroes. At the same time we seek to make further progress in the description of the asymptotic structure of the hyperKaehler metric these moduli spaces come equipped with. These results relate and will find possible applications to such diverse analytic-geometrical objects as gravitational instantons (which in some cases arise as Higgs bundle moduli spaces) and equivariant harmonic maps which play a crucial role in nonabelian Hodge theory.

本文的主题是希格斯束的模空间及其渐近几何。在这里，我们打算更好地理解Hitchin的自对偶方程在解属于多零全纯二次微分的情况下的奇异紧化。同时，我们寻求在描述这些模空间所配备的超kaehler度量的渐近结构方面取得进一步进展。这些结果与诸如引力瞬子（在某些情况下以希格斯束模空间出现）和在非阿贝尔霍奇理论中起关键作用的等变调和映射等各种分析几何对象相关，并将找到可能的应用。