nLab
Klein quadric

Contents

Idea

A projective variety that is moreover a quadric given by zeroes of the quadratic form

x 0x 5+x 1x 4+x 2x 3 x_0x_5 + x_1 x_4 + x_2 x_3

where [x 0:x 1:x 2:x 3:x 4:x 5][x_0:x_1:x_2:x_3:x_4:x_5] are homogeneous coordinates on 5\mathbb{P}^5. It was studied in (Klein 1868), together with what is now called the Klein correspondence?, by Felix Klein in his 1868 dissertation under Julius Plücker?.

Properties

The conformal compactification, of complexified Minkowski spacetime 3,1\mathbb{R}^{3,1}, is given by the Klein quadric. (eg, Fioresi-Lledo-Varadarajan 07, section 2).

References

Last revised on July 29, 2016 at 03:55:14. See the history of this page for a list of all contributions to it.