Espace des modules des faisceaux semi-stables de rang 2 et de classes de Chern $c_{1}=0$, $c_{2}=2$ et $c_{3}=0$ sur une hypersurface cubique lisse de $\mathbb{P}^{4}$

Abstract

In this note we study the moduli space of rank two semistable sheaves on a smooth cubic hypersurface $X\subset\mathbb{P}^{4}$ with $c_{1}=0$, $c_{2}=2$ and $c_{3}=0$. We show that it is isomorphic to the blow-up of the intermediate jacobian $J(X)$ of $X$ along the Fano surface of $X$. We complete previous results of Iliev-Markushevich AG/9910058 and Markushevich-Tikhomirov AG/9910063.