I'm trying to understand the claim that the moduli space of stable rank 2 vector bundles on a (general?) cubic 3-fold, say $X$, with $deg c_2=6$ and $det=O_X(2)$ is of dimension 9.
I belive what I can do, is to compute the tangent space at a general point, says $E$, and try to compute its dimension, and I seem to recall that this can be done by computing the $H^1$ of a certain bundle ($End(E)?$) but I haven't managed to find any specific reference for that fact.
Is it correct? And if so, where does that come from?