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.
Other articles related to "rational variety, variety, rational":
... A rationally connected variety V is a projective algebraic variety over an algebraically closed field such that through every two points there passes the image of a regular ... Equivalently, a variety is rationally connected if every two points are connected by a rational curve contained in the variety ... as the only algebraic curves which are rationally connected are the rational ones ...
Famous quotes containing the words variety and/or rational:
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—Mary Wortley, Lady Montagu (16891762)
“There has never been in history another such culture as the Western civilization M a culture which has practiced the belief that the physical and social environment of man is subject to rational manipulation and that history is subject to the will and action of man; whereas central to the traditional cultures of the rivals of Western civilization, those of Africa and Asia, is a belief that it is environment that dominates man.”
—Ishmael Reed (b. 1938)