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SIGMA 6 (2010), 006, 13 pages arXiv:0802.2438
https://doi.org/10.3842/SIGMA.2010.006
Peterson's Deformations of Higher Dimensional Quadrics
Ion I. Dincă
Faculty of Mathematics and Informatics, University of Bucharest, 14 Academiei Str., 010014, Bucharest, Romania
Received July 13, 2009, in final form January 16, 2010; Published online January 20, 2010
Abstract
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
C3 of 2-dimensional general quadrics with common
conjugate system given by the spherical coordinates on the complex
sphere S2 ⊂ C3 to an explicit
(n–1)-dimensional family of deformations in C2n–1
of n-dimensional general quadrics with common conjugate system
given by the spherical coordinates on the complex sphere
Sn ⊂ Cn+1 and non-degenerate joined
second fundamental forms. It is then proven that this family is
maximal.
Key words:
Peterson's deformation; higher dimensional quadric; common conjugate system.
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