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:
“The fire is the main comfort of the camp, whether in summer or winter, and is about as ample at one season as at another. It is as well for cheerfulness as for warmth and dryness.”
—Henry David Thoreau (1817–1862)
“I fear I agree with your friend in not liking all sermons. Some of them, one has to confess, are rubbish: but then I release my attention from the preacher, and go ahead in any line of thought he may have started: and his after-eloquence acts as a kind of accompaniment—like music while one is reading poetry, which often, to me, adds to the effect.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“In the quilts I had found good objects—hospitable, warm, with soft edges yet resistant, with boundaries yet suggesting a continuous safe expanse, a field that could be bundled, a bundle that could be unfurled, portable equipment, light, washable, long-lasting, colorful, versatile, functional and ornamental, private and universal, mine and thine.”
—Radka Donnell-Vogt, U.S. quiltmaker. As quoted in Lives and Works, by Lynn F. Miller and Sally S. Swenson (1981)