In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold 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.
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Famous quotes containing the words ample, line and/or bundle:
“I’ve known her—from an ample nation—
Choose One—
Then—close the Valves of her attention—
Like Stone—”
—Emily Dickinson (1830–1886)
“Today, the notion of progress in a single line without goal or limit seems perhaps the most parochial notion of a very parochial century.”
—Lewis Mumford (1895–1990)
““There is Lowell, who’s striving Parnassus to climb
With a whole bale of isms tied together with rhyme,
He might get on alone, spite of brambles and boulders,
But he can’t with that bundle he has on his shoulders,
The top of the hill he will ne’er come nigh reaching
Till he learns the distinction ‘twixt singing and preaching;”
—James Russell Lowell (1819–1891)