Dual Projective Space
When the construction above is applied to the dual space V* rather than V, one obtains the dual projective space, which can be canonically identified with the space of hyperplanes through the origin of V. That is, if V is n dimensional, then P(V*) is the Grassmannian of n−1 planes in V.
In algebraic geometry, this construction allows for greater flexibility in the construction of projective bundles. One would like to be able associate a projective space to every quasi-coherent sheaf E over a scheme Y, not just the locally free ones. See EGAII, Chap. II, par. 4 for more details.
Read more about this topic: Projective Space
Famous quotes containing the words dual and/or space:
“Thee for my recitative,
Thee in the driving storm even as now, the snow, the winter-day
declining,
Thee in thy panoply, thy measur’d dual throbbing and thy beat
convulsive,
Thy black cylindric body, golden brass and silvery steel,”
—Walt Whitman (1819–1892)
“Oh, my. I’d forgotten how much I hate space travel.”
—George Lucas (b. 1944)