Déformations des extensions larges de faisceaux .  Pacific Journal of Mathematics 220, 2 (2005), 201-297.

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. Strømme 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.

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