Nontrivial linear projections on the Grassmannian Gr3(C6)

Typically, a linear projection of the Grassmannian in its Plücker embedding is generically injective, unless image space. A notable exception are self-adjoint projections, which have even degree. We consider projections Gr3C6 with low-dimensional centers projection. When center has dimension less than five, we show that degree 1. five and greater 1, it self-adjoint.