  We consider double determinantal varieties, a special case of Nakajima quiver
varieties. Li conjectured that double determinantal varieties are normal,
irreducible, Cohen-Macaulay varieties whose defining ideals have a Gr\"obner
basis given by their natural generators. We use liaison theory to prove this
conjecture in a manner that generalizes results for mixed ladder determinantal
varieties. We also give a formula for the dimension of a double determinantal
variety.
