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.
