Maximum 2-rank webs AGW(6, 3, 2)

Maximum rank webs are not necessarily almost Grassmannizable

“…While looking recently at the paper [5], the author of the present paper recognized the importance of the referee counterexample. This counterexample looks easy but it is not trivial and was not known so far.…”

“…The coefficients λ a1 and λ a2 in (4) satisfy certain inequalities which are implied by the fact that the system of equations ( 1), (2), and ( 5) must be solvable with respect to any six forms [5]).…”

“…When Goldberg presented for publication the first version of his paper [5], where he considered the maximum rank webs W (6, 3, 2), he applied the above Little's result and deduced that these kind of webs are always almost Grassmannizable.…”

“…In the revised version of the paper [5], Goldberg changed the reference to Little's paper [7] by the additional assumption that the maximum rank webs W (d, n, r) in question are almost Grassmannizable.…”

“…Consider 4-subwebs [4,1,2,3], [5,1,2,3], and [6,1,2,3] defined by the first three foliations X 1 , X 2 , X 3 of a web W (6, 3, 2) and the foliations X 4 , X 5 , and X 6 , respectively. Each of these 4-subwebs defines an almost Grassmann structure.…”