In the proof Proposition 8.4 we need to show that if Z is fifteen points in the plane defined by the (5x5)minors of a general (5x6) matrix of linear forms, then there are no curves of degree 8, singular along Z.






In Y, a smooth 4fold in $\mathbb{P}^7$ defined as the rank 2 locus of (3x5) matrix M of linear forms, let S1 be the 3fold scroll defined as the rank 1 locus of the submatrix M12 of M consisting of its two first rows, and let S2 be the 3fold scroll defined as the rank 1 locus of the submatrix M23 of M consisting of its two last rows Then we show that every cubic hypersurface that contains both S1 and S2, contains all of Y. Hence this is the case for any divisor on Y equivalent to S1+S2.









