This is a homogeneous equation of degree 2, and hence its solutions lie on a four-dimensional quadric hypersurface in real projective 5-space.''
Ha! I love how it will take me hours to understand/believe that statement, and the author of my thesis book just gets to throw it out there with the word "hence." But, at least it's not complex projective 5-space. that would suck more. i think.
TeX markup for your (and my) pleasure.