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On the algebraic models of symmetric smooth manifolds
-
R. Ghiloni
and
A. Tancredi
Published/Copyright:
July 8, 2014
Abstract
Let M be a compact smooth submanifold of ℝn that is symmetric with respect to an affine subspace L. In this paper, we prove that M has a symmetric Nash model N, which is unique up to Nash isomorphism preserving symmetries. Such a model N can be chosen to be a union of nonsingular connected components of a real algebraic set if M is a (not necessarily compact) Nash submanifold of ℝn. If M does not intersect the mirror L, then we are able to construct a symmetric algebraic model of M too. More precisely, in this case, we show that the set of birationally nonisomorphic symmetric algebraic models of M has the power of continuum.
Keywords: Algebraic models of smooth manifolds; smooth manifolds with symmetries; affine Nash manifolds; nonsingular real algebraic sets
Published Online: 2014-7-8
Published in Print: 2014-7-1
© 2014 by Walter de Gruyter Berlin/Boston
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Keywords for this article
Algebraic models of smooth manifolds;
smooth manifolds with symmetries;
affine Nash manifolds;
nonsingular real algebraic sets
Articles in the same Issue
- Masthead
- On axiomatic definitions of non-discrete affine buildings
- On Clifford analysis for holomorphic mappings
- Universal points of convex bodies and bisectors in Minkowski spaces
- The equal tangents property
- Some theorems of harmonic maps for Finsler manifolds
- The regular Grünbaum polyhedron of genus 5
- On the existence of nilsolitons on 2-step nilpotent Lie groups
- Rotational linear Weingarten hypersurfaces in the Euclidean sphere Sn+1
- Spacelike hypersurfaces in anti-de Sitter space
- The group of strong symplectic homeomorphisms in the L∞-metric
- The total Betti number of the intersection of three real quadrics
- On the algebraic models of symmetric smooth manifolds
- Non-existence of tight neighborly triangulated manifolds with β1 = 2
