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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.

4 votes

Intersection of Subspaces with $O(3)$

In general the answer is no. For example, the matrices whose first column is a column of zeroes form a $6-$dimensional subspace not containing any ortogonal matrix, because it does not contain any inv …
Roberto Pignatelli's user avatar