On Surjective Quadratic Maps from \(\boldsymbol{\mathbb{P}}^{\mathbf{3}}\) to \(\boldsymbol{\mathbb{P}}^{\mathbf{2}}\)

In this article, we give the criterion of surjectivity ofquadratic maps from \({\mathbb{P}}^{3}\) to \({\mathbb{P}}^{2}\) . Usingthis criterion, we prove that surjective quadratic maps form aZariski-open subset in the space of dominant quadratic maps.