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We study the degrees of generators of the ideal of a projected Veronesevariety $v_2(\mathbb{P}^3)\subset \mathbb{P}^9$ to $\mathbb{P}^6$ depending onthe center of projection. This is related to the geometry of zero dimensionalschemes 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$\mathbb{P}^6$.

Smoothable zero dimensional schemes and special projections of algebraic varieties