The moduli space of curves is rigid

Hacking, Paul

doi:10.2140/ant.2008.2.809

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The moduli space of curves is rigid

Paul Hacking

Vol. 2 (2008), No. 7, 809–818

DOI: 10.2140/ant.2008.2.809

Abstract

We prove that the moduli stack ${\bar{ℳ}}_{g, n}$ 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.

Keywords

moduli, curve, rigidity

Mathematical Subject Classification 2000

Primary: 14H10

Milestones

Received: 30 November 2007

Revised: 6 August 2008

Accepted: 17 September 2008

Published: 23 November 2008

Authors

Paul Hacking
Department of Mathematics University of Washington Box 354350 Seattle, WA 98195-4350 United States
http://www.math.washington.edu/~hacking/

Vol. 2, No. 7, 2008