Peterson's Deformations of Higher Dimensional Quadrics

We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in C^3 of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere S^2 subset C^3 to an explicit (n–1)-dimensional family of deformations in C^{2n–1} of n-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere S^n subset C^{n+1} and non-degenerate joined second fundamental forms. It is then proven that this family is maximal.