Deformations des extensions larges de faisceaux

Let X be a projective smooth irreducible polarized variety over the field of complex numbers. Typical examples of wide extensions are vector bundles E that have a subsheaf F whose slope is much bigger than the slope of E/F, and such that F and E/F are stable. We study the deformations of such bundles. The case of unstable rank 2 bundles has been considered by S.A. Stromme on P_2, and by C. Banica on P_3. We build moduli spaces of wide extensions, and if the dimension of X is greater than 2, it may even happen that we obtain fine moduli spaces.