Vol. 2, No. 7, 2008

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The moduli space of curves is rigid

Paul Hacking

Vol. 2 (2008), No. 7, 809–818
Abstract

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.

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/