## Algebra & Number Theory

### The moduli space of curves is rigid

Paul Hacking

#### Abstract

We prove that the moduli stack $ℳ¯g,n$ 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

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

Dates
Revised: 6 August 2008
Accepted: 17 September 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513797320

Digital Object Identifier
doi:10.2140/ant.2008.2.809

Mathematical Reviews number (MathSciNet)
MR2460695

Zentralblatt MATH identifier
1166.14019

Subjects
Primary: 14H10: Families, moduli (algebraic)

Keywords
moduli curve rigidity

#### Citation

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. https://projecteuclid.org/euclid.ant/1513797320

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