Stable bundles of rank 2 with Chern's classes $c_1=0$, $c_2=2$ on $\mathbb P^3$ and Poncelet hyperquadrics

In this article we investigate the variety $M(0,2)$ of stable vector bundles of rank 2 on $\mathbb P^3$ with Chern's classes $c_1=0$, $c_2=2$ and give the explicit description of closure of $M(0,2)$ as the intersection of special determinantal locus with uniquely determined Poncelet hyperquadric in $\mathbb P^{20}$.