The moduli space of curves is rigid

Details The moduli space of curves is rigid The moduli space of curves is rigid

2005-09-23

arxiv.org/abs/math/0509567v2

Algebra and Number Theory 2 (2008), no. 7, 809--818

Mathematics

Algebraic Geometry

11 pages. v2: Proof rewritten to avoid use of log structures. Example of nonrigid moduli space of surfaces added

Scientific paper

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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