ON EQUATION VERIFIED BY INVARIANTS OF EXC EPTIONAL VECTOR-BUNDLES

The helices and foundations of exceptional vector bundles on IF, have been defined by A.L. Gorodentsev and A.N. Rudakov. D.Y. Nogin has foun d some relations among the invariants of the exceptional bundles in fo undations of helices (E(0), E(1), E(2), E(3)). The main result of this paper is that the only algebraic relations among the squares of the r anks of the E(i)'s and the invariants Delta(1)(E(i)), Delta(2)(E(i)), Delta(3)(E(i)) (also defined here) can be deduced from some ''obvious' ' relations. To prove this, an algebraic projective variety Z associat ed to foundations of helices is defined. It contains them as closed po ints. Another construction of Z is given, using plane curves associate d to exceptional bundles and their geometry.