Nonisomorphic algebraic models of a smooth manifold with group action

Dovermann, Karl Heinz; Masuda, Mikiya; Suh, Dong Youp

doi:10.1090/S0002-9939-1995-1219723-8

Nonisomorphic algebraic models of a smooth manifold with group action
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by Karl Heinz Dovermann, Mikiya Masuda and Dong Youp Suh PDF

Proc. Amer. Math. Soc. 123 (1995), 55-61 Request permission

Abstract:

Let G be a finite group and M a closed smooth G manifold. If M has any equivariant algebraic model, then we show that it has uncountable many birationally inequivalent such models. This generalizes a non-equivariant result of Bochnak and Kucharz.

References

Selman Akbulut and Henry C. King, The topology of real algebraic sets with isolated singularities, Ann. of Math. (2) 113 (1981), no. 3, 425–446. MR 621011, DOI 10.2307/2006992
J. Bochnak and W. Kucharz, Nonisomorphic algebraic models of a smooth manifold, Math. Ann. 290 (1991), no. 1, 1–2. MR 1107659, DOI 10.1007/BF01459234
Karl Heinz Dovermann, Friedrich Knop, and Dong Youp Suh, Topological invariants of real algebraic actions, Topology Appl. 40 (1991), no. 2, 171–188. MR 1123261, DOI 10.1016/0166-8641(91)90049-R
Karl Heinz Dovermann and Mikiya Masuda, Algebraic realization of manifolds with group actions, Adv. Math. 113 (1995), no. 2, 304–338. MR 1337110, DOI 10.1006/aima.1995.1040
Karl Heinz Dovermann, Mikiya Masuda, and Dong Youp Suh, Algebraic realization of equivariant vector bundles, J. Reine Angew. Math. 448 (1994), 31–64. MR 1266746, DOI 10.1090/conm/182/02084
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
Sung Sook Kim and Mikiya Masuda, Topological characterization of nonsingular real algebraic $G$-surfaces, Topology Appl. 57 (1994), no. 1, 31–39. MR 1271332, DOI 10.1016/0166-8641(94)90030-2

Abelian varieties

Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. MR 817210, DOI 10.1007/978-1-4757-1920-8
A. Tognoli, Su una congettura di Nash, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 27 (1973), 167–185. MR 396571
Hassler Whitney, Elementary structure of real algebraic varieties, Ann. of Math. (2) 66 (1957), 545–556. MR 95844, DOI 10.2307/1969908