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.

• Wonderful compactification
• Homogeneous variety
• Spherical variety

• 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