Local rigidity of covering constructions and Weil--Petersson subvarieties of the moduli space of curves
Year: 2025
Type: preprint
Abstract: 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 $\mathcal M_{g,n}$.
Source: arXiv (Cornell University)
Author: Serván, Carlos A.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7084626009
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