Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914064917069824 |
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| author | Serván, Carlos A. |
| author_facet | Serván, Carlos A. |
| contents | We show that totally geodesic subvarieties of the moduli space $\mathcal M_{g,n}$ of genus $g$ curves with $n$ marked points, endowed with the Weil--Petersson metric, are locally rigid. This implies that covering constructions -- examples of totally geodesic subvarieties of $\mathcal M_{g,n}$ endowed with the Teichmüller metric -- are locally rigid. We deduce the local rigidity statement from a more general rigidity result for a class of orbifold maps to $\mathcal M_{g,n}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_25523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves Serván, Carlos A. Geometric Topology Algebraic Geometry Complex Variables We show that totally geodesic subvarieties of the moduli space $\mathcal M_{g,n}$ of genus $g$ curves with $n$ marked points, endowed with the Weil--Petersson metric, are locally rigid. This implies that covering constructions -- examples of totally geodesic subvarieties of $\mathcal M_{g,n}$ endowed with the Teichmüller metric -- are locally rigid. We deduce the local rigidity statement from a more general rigidity result for a class of orbifold maps to $\mathcal M_{g,n}$. |
| title | Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves |
| topic | Geometric Topology Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2509.25523 |