Hodge numbers of moduli of principal bundles on a curve
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866916061815767040 |
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| author | Liu, Chiu-Chu Melissa Schaffhauser, Florent |
| author_facet | Liu, Chiu-Chu Melissa Schaffhauser, Florent |
| contents | We prove an inversion theorem for recursive formulas satisfied by certain families of converging power series in two variables. These power series are indexed by the Harder-Narasimhan types of principal $G$-bundles of degree $d \in π_1 G$ on a smooth projective curve $X$, where $G$ is a connected complex reductive group. As an application, we obtain a closed formula for the Hodge-Poincaré series of moduli stacks of semistable principal $G$-bundles of degree $d$. We also compute the variation of Hodge structure of the moduli stack of all principal $G$-bundles over $X$, as a function of the period matrix of that curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hodge numbers of moduli of principal bundles on a curve Liu, Chiu-Chu Melissa Schaffhauser, Florent Algebraic Geometry 14D23, 14C30 We prove an inversion theorem for recursive formulas satisfied by certain families of converging power series in two variables. These power series are indexed by the Harder-Narasimhan types of principal $G$-bundles of degree $d \in π_1 G$ on a smooth projective curve $X$, where $G$ is a connected complex reductive group. As an application, we obtain a closed formula for the Hodge-Poincaré series of moduli stacks of semistable principal $G$-bundles of degree $d$. We also compute the variation of Hodge structure of the moduli stack of all principal $G$-bundles over $X$, as a function of the period matrix of that curve. |
| title | Hodge numbers of moduli of principal bundles on a curve |
| topic | Algebraic Geometry 14D23, 14C30 |
| url | https://arxiv.org/abs/2605.30223 |