Abstract

For any odd n, we prove that the coherent sheaf FA on PCn, defined as the cokernel of an injective map f : OPn⊕2 →OPn(1)⊕(n+2), is Mumford-Takemoto stable if and only if the map f is stable, when considered as a point of the projective space P(Hom(OPn×2,OPn×(n+2))*) under the action of the reductive group SL(2) × SL(n + 2). This proves a particular case of a conjecture of J.-M.Drezet and it implies that a component of the Maruyama scheme of the semi-stable sheaves on Pn of rank n and Chern polynomial (1 + t)n+2 is isomorphic to the Kronecher moduli N(n + 1,2,n + 2), for any odd n. In particular, such scheme defines a smooth minimal compactification of the moduli space of the rational normal curves in Pn, that generalizes the construction defined by G. Ellinsgrud, R. Piene and S. Strømme in the case n = 3.

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