In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to
the field of all rational functions for some set of indeterminates, where d is the dimension of the variety.
Read more about Rational Variety: Rationality and Parameterization, Rationality Questions, Classical Results, Unirationality, Rationally Connected Variety
Famous quotes containing the words rational and/or variety:
“... how can a rational being be ennobled by any thing that is not obtained by its own exertions?”
—Mary Wollstonecraft (1759–1797)
“Uses are always much broader than functions, and usually far less contentious. The word function carries overtones of purpose and propriety, of concern with why something was developed rather than with how it has actually been found useful. The function of automobiles is to transport people and objects, but they are used for a variety of other purposes—as homes, offices, bedrooms, henhouses, jetties, breakwaters, even offensive weapons.”
—Frank Smith (b. 1928)