Algebraic Geometry
In algebraic geometry, the normal bundle NXY of a regular embedding i: X → Y, defined by some sheaf of ideals I is the vector bundle on X corresponding to the dual of the sheaf I/I2. The regularity of the embedding ensures that this sheaf is locally free and agrees with the normal cone CXY, which is defined as .
Read more about this topic: Normal Bundle
Famous quotes containing the words algebraic and/or geometry:
“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
—Henry David Thoreau (1817–1862)
“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”
—Louise Bourgeois (b. 1911)