The equations of type II1 unprojection

The type II1 unprojection is, by definition, the generic complete intersection type II unprojection, in the sense of [S. Papadakis, Type II unprojection, J. Algebraic Geometry 15 (2006) 399–414, Section 3.1], for the parameter value k=1k=1, and depends on a parameter n≥2n≥2. Our main results are the explicit calculation of the linear relations of the type II1 unprojection for any value n≥2n≥2 and the explicit calculation of the quadratic equation for the case n=3n=3 given in two theorems respectively. In addition, one of the sections contains applications to algebraic geometry.