Fibers of the Blow up of $\mathbb{A}^6$ over the center defined by ideal defined by vanishing of rank two minors.

Question

Let us consider set of all matrices \begin{pmatrix}{} x & u & v \\ u & y & w \\ v & w & z \end{pmatrix} where $x,y,z,u,v,w\in \mathbb{R}$ which is equivalent to $\mathbb{A}^6$.

Consider the sub-variety $V$ defined by vanishing of the rank two minors of the matrix.

$V=\{(x,y,z,u,v,w):xy-u^2=0,yz-w^2=0,xz-v^2=0,xw-uv=0,uw-vy=0, uz-vw=0\}$

Let's say we blow up $\mathbb{A}^6$ along $V$.

My question is can we describe the fibers of the blow-up over the center?