On the moduli space of the Schwarzenberger bundles

Abstract

By proving a particular case of a conjecture of Drezet, we show that a component of the Maruyama scheme of the semi-stable sheaves on the projective space $\PP^n$ 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 $\PP^n$, that generalizes the construction defined by G. Ellinsgrud, R. Piene and S. Strømme in the case $n=3$.