The intersection of three quadrics in P^7 revisited

We show that the natural nc-space attached to an intersection of three quadrics in P^7 is truly non-commutative. In particular, its associated numerical K-lattice is not isomorphic to the K-lattice of any smooth projective surface, so the relevant derived category is not equivalent to the derived category of any smooth projective surface. Using the new theory of Hodge atoms, this reproves the irrationality of a very general intersection of three quadrics in P7.