**Preamble**

I initially decided to post this question on math.stackexchange a few days ago, as I consider it to be much less of a research question and much more of "I'm learning" question. But there weren't any takers, and since then it's naturally slipped farther down the "Questions" list over there. So I'm trying my luck here instead.$^*$

**Question**

Does anyone know of a nice way to think about endomorphisms of vector bundles arising from the Serre construction/correspondence---that is, the vector bundles on projective varieties associated to codimension 2 subvarieties? I am interested in particular in the case of such bundles on $\mathbb{CP}^2$, where these bundles have sections vanishing on prescribed sets of points. Is there anything concrete we can say about elements of $\Gamma(\mathbb{CP}^2,\mbox{End} E)$ when E is one of these bundles?

**General Motivation**

I'm learning about vector bundle constructions, and I'm trying to compute the cohomologies of these constructions, namely $H^i(E)$ and $H^i(\mbox{End}(E))$.

$^*$ In order to maintain tidiness, I will remove the duplicate question from math.stackexchange if it seems to generate more activity here.