A desingularization of real differentiable actions of finite groups

Details A desingularization of real differentiable actions of finite groups A desingularization of real differentiable actions of finite groups

2003-09-17

arxiv.org/abs/math/0309280v2

IMRN 2005:15 (2005) 881-898.

Mathematics

Algebraic Geometry

14 pages, 3 figures; substantial revision of Section 4, minor corrections elsewhere, to appear in IMRN

Scientific paper

We provide abelianizations of differentiable actions of finite groups on smooth real manifolds. De Concini-Procesi wonderful models for (local) subspace arrangements and a careful analysis of linear actions on real vector spaces are at the core of our construction. In fact, we show that our abelianizations have stabilizers isomorphic to elementary abelian 2-groups, a setting for which we suggest the term digitalization. As our main examples, we discuss the resulting digitalizations of the permutation actions of the symmetric group on real linear and projective spaces.

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