Symmetric variety

Mathematical concept

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In algebraic geometry, a symmetric variety is an algebraic analogue of a symmetric space in differential geometry, given by a quotient G/H of a reductive algebraic group G by the subgroup H fixed by some involution of G.

## See also

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* Wonderful compactification
* Homogeneous variety
* Spherical variety

## References

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* Ash, A.; Mumford, David; Rapoport, M.; Tai, Y. (1975), Smooth compactification of locally symmetric varieties (PDF), Brookline, Mass.: Math. Sci. Press, ISBN 978-0-521-73955-9, MR 0457437

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