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arXiv · 2609.13337

Stringy invariants for abelian character varieties

Carlos Florentino·Ángel González-Prieto·Alfonso Zamora
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Abstract

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.

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Carlos Florentino, Ángel González-Prieto, Alfonso Zamora. 2026-09-17. Stringy invariants for abelian character varieties. https://arxiv.org/abs/2609.13337

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