  We study the degrees of generators of the ideal of a projected Veronese
variety $v_2(\mathbb{P}^3)\subset \mathbb{P}^9$ to $\mathbb{P}^6$ depending on
the center of projection. This is related to the geometry of zero dimensional
schemes of length $8$ in $\mathbb{A}^4$, Cremona transforms of $\mathbb{P}^6$,
and the geometry of Tonoli Calabi-Yau threefolds of degree $17$ in
$\mathbb{P}^6$.
