Line Bundle/invertible Sheaf Language
Linear systems are still at the heart of contemporary algebraic geometry; but they are typically introduced by means of the line bundle or invertible sheaf language. That is, the language of sheaf theory is considered the most natural starting point, at least to learn the theory. In those terms, divisors D (Cartier divisors, importantly) correspond to line bundles, and linear equivalence of two divisors means that the corresponding line bundles are isomorphic.
Read more about this topic: Linear System Of Divisors
Famous quotes containing the words line, bundle and/or language:
“For a woman to get a rewarding sense of total creation by way of the multiple monotonous chores that are her daily lot would be as irrational as for an assembly line worker to rejoice that he had created an automobile because he tightened a bolt.”
—Edith Mendel Stern (1901–1975)
“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)
“Man, even man debased by the neocapitalism and pseudosocialism of our time, is a marvelous being because he sometimes speaks. Language is the mark, the sign, not of his fall but of his original innocence. Through the Word we may regain the lost kingdom and recover powers we possessed in the far-distant past.”
—Octavio Paz (b. 1914)