Algebra & Number Theory

The moduli space of curves is rigid

Paul Hacking

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We prove that the moduli stack ¯g,n of stable curves of genus g with n marked points is rigid, that is, 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.

Article information

Algebra Number Theory, Volume 2, Number 7 (2008), 809-818.

Received: 30 November 2007
Revised: 6 August 2008
Accepted: 17 September 2008
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)

moduli curve rigidity


Hacking, Paul. The moduli space of curves is rigid. Algebra Number Theory 2 (2008), no. 7, 809--818. doi:10.2140/ant.2008.2.809.

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