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There are exactly four surfaces of minimal degree in P 5 , up to projective equivalence. And they have the same graded Betti numbers. So it is a natural question to ask how to recognize them by their defining equations. In this paper we provide an answer to this question in terms of the rank loci of quadratic equations of those four surfaces. We show that the sets of rank 3 and rank 4 quadratic equations distinguish them.
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