The 4 Subspace Problem
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We present a complete solution to the 4 subspace problem in the generality of an algebraically closed eld. We do this by means of Auslander-Reiten theory and give the Auslander-Reiten quiver of the extended $D_4$ Dynkin diagram. We also give a geometric interpretation when two congurations of four lines through the origin in the plane are equivalent.