Peterson's Deformations of Higher Dimensional Quadrics

Details Peterson's Deformations of Higher Dimensional Quadrics Peterson's Deformations of Higher Dimensional Quadrics

2008-02-18

arxiv.org/abs/0802.2438v8

SIGMA 6 (2010), 006, 13 pages

Mathematics

Differential Geometry

Scientific paper

10.3842/SIGMA.2010.006

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 $\mathbb{C}^3$ of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere $\mathbb{S}^2\subset\mathbb{C}^3$ to an explicit $(n-1)$-dimensional family of deformations in $\mathbb{C}^{2n-1}$ of $n$-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere $\mathbb{S}^n\subset\mathbb{C}^{n+1}$ and non-degenerate joined second fundamental forms. It is then proven that this family is maximal.

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