[B.sub.MA] is indeed the residual in a quadratic congruence of the union of a subgrassmannian G(1, L) (where L is a [P.sup.3]) with a congruence of multidegree (1, 3, 0) contained in a very special linear congruence. In particular [B.sub.MA] is not a linear congruence.
Finally, we observe that the lines of B, passing through a point P, not in L, of the focal locus X, form a planar pencil since B is contained in a linear congruence (as in Proposition 4.2 of [DM05]), or by Lemma 4(3).
We compare [B.sub.Q] with a linear congruence, whose multidegree is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
V Ferapontov, Systems of conservation laws of Temple class, equations of associativity and linear congruences in [P.sup.4], Manuscripta Math.