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The moduli space of curves is rigid

Paul Hacking
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Abstract

We prove that the moduli stack of stable curves of genus g with n marked points is rigid, i.e., has no infinitesimal deformations. This confirms the first case of a principle proposed by Kapranov. It can also be viewed as a version of Mostow rigidity for the mapping class group.

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Paul Hacking. 2008-08-28. The moduli space of curves is rigid. https://arxiv.org/abs/math/0509567

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