Dictionary Meaning and Definition on 'Ample'
- more than enough in size or scope or capacity; "had ample food for the party"; "an ample supply" [ant: meager]
- affording an abundant supply; "had ample food for the party"; "copious provisions"; "food is plentiful"; "a plenteous grape harvest"; "a rich supply" [syn: copious, plenteous, plentiful, rich]
- fairly large; "a sizable fortune"; "an ample waistline"; "of ample proportions" [syn: sizable, sizeable]
- Ample \Am"ple\, a. [F. ample, L. amplus, prob. for ambiplus full
on both sides, the last syllable akin to L. plenus full. See
Full, and cf. Double.]
Large; great in size, extent, capacity, or bulk; spacious;
roomy; widely extended.
All the people in that ample house Did to that image
bow their humble knees. --Spenser.
- Fully sufficient; abundant; liberal; copious; as, an ample fortune; ample justice.
- Not contracted of brief; not concise; extended; diffusive; as, an ample narrative. --Johnson. Syn: Full; spacious; extensive; wide; capacious; abundant; plentiful; plenteous; copious; bountiful; rich; liberal; munificent. Usage: Ample, Copious, Abundant, Plenteous. These words agree in representing a thing as large, but under different relations, according to the image which is used. Ample implies largeness, producing a sufficiency or fullness of supply for every want; as, ample stores or resources, ample provision. Copious carries with it the idea of flow, or of collection at a single point; as, a copious supply of materials. ``Copious matter of my song.'' --Milton. Abundant and plenteous refer to largeness of quantity; as, abundant stores; plenteous harvests.
Wikipedia Meaning and Definition on 'Ample'
In algebraic geometry, a very ample line bundle L is one with enough sections to set up an embedding of its base variety or manifold M into projective space. An ample line bundle is one such that some positive power is very ample. Globally generated sheaves are those with enough sections to define a morphism to projective space.
Let X be a scheme or a complex manifold and F a sheaf on X. One says that F is generated by (finitely many) global sections , if every stalk of F is generated by the germs of the ai. For example, if F happens to be a line bundle, i.e. locally free of rank 1, this amounts to having finitely many global sections, such that for any point x in X, there is at least one section not vanishing at this point. In this case a choice of such global generators a0, ..., an gives a morphism[See more about Ample at Dictionary 3.0 Encyclopedia]
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