发表机构
Faculdade de Ciências, Univ. de Lisboa; Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid; Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UC3M); Universidad Politécnica de Madrid（里斯本大学理学院; 马德里康普顿斯大学数学科学学院; 数学科学研究所; 马德里理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文计算了自由阿贝尔群特征簇与阿贝尔簇上Higgs丛模空间的所有弦论不变量，证明朗兰兹对偶群的不变量相等，并指出辛解消仅存在于Dynkin类型A、B、C的情形。
AI 中文摘要
我们计算了所有弦论不变量，这些不变量编码了自由阿贝尔群的$G$-特征簇的单位连通分支（的规范化）以及阿贝尔簇上$G$-Higgs丛模空间的轨道折叠上同调数，适用于所有复连通约化群$G$。作为应用，我们提供了拓扑镜像对称陈述的直接证明：朗兰兹对偶群的弦论不变量相等。在Ginzburg--Kaledin局部解消的框架下，我们讨论了这些弦论不变量的含义，表明这些模空间的辛解消仅存在于Dynkin类型为$A$、$B$或$C$的群的情形。当此类解消存在时，计算出的弦论Hodge数与解消的实际Hodge数一致。
英文摘要
We compute all stringy invariants, encoding orbifold cohomology numbers, of (the normalization of) the identity component of $G$-character varieties of free abelian groups and of moduli spaces of $G$-Higgs bundles on abelian varieties, for all complex connected reductive groups $G$. As an application, we provide a direct proof of a topological mirror symmetry statement: the equality of the stringy invariants for Langlands dual groups. In the framework of Ginzburg--Kaledin local resolutions, we discuss the meaning of these stringy invariants, showing that symplectic resolutions of these moduli spaces can only exist in the cases of groups of Dynkin type $A$, $B$, or $C$. When such resolutions exist, the computed stringy Hodge numbers agree with the actual Hodge numbers of the resolution.
Comments35 pp. (plus 21 pp. appendix). Comments are welcome
