The helices and foundations of helices of exceptional bundles on  have been defined by A.L. Gorodentsev and A.N. Rudakov.   D.Y. Nogin found some relations among the invariants of the exceptional bundles in foundations of helices (E₀,E₁,E₂,E₃). The main result of this paper is that the only relations among the squares of the ranks of the E_i's and their invariants , ,  (also defined here) can be deduced from some "obvious" relations. To prove this an algebraic projective variety Z associated to foundations of helices is defined. It contains them as closed points, and we prove that the smallest closed subvariety containing all these closed points is Z. Another construction of Z is given, using plane curves naturally associated to exceptional bundles and their geometry.

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