Peterson's Deformations of Higher Dimensional Quadrics

[摘要] 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 ⊂ C 3 to an explicit ( n –1)-dimensional family of deformations in C 2 n –1 of n -dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere S n ⊂ C n +1 and non-degenerate joined second fundamental forms. It is then proven that this family is maximal.

[关键词] Peterson’s deformation;higher dimensional quadric;common conjugate system