Connection To Picard Variety
The Albanese variety is dual to the Picard variety (the connected component of zero of the Picard scheme classifying invertible sheaves on V):
For algebraic curves, the Abel–Jacobi theorem implies that the Albanese and Picard varieties are isomorphic.
Read more about this topic: Albanese Variety
Famous quotes containing the words connection to, connection and/or variety:
“One must always maintain one’s connection to the past and yet ceaselessly pull away from it. To remain in touch with the past requires a love of memory. To remain in touch with the past requires a constant imaginative effort.”
—Gaston Bachelard (1884–1962)
“We live in a world of things, and our only connection with them is that we know how to manipulate or to consume them.”
—Erich Fromm (1900–1980)
“In different hours, a man represents each of several of his ancestors, as if there were seven or eight of us rolled up in each man’s skin,—seven or eight ancestors at least, and they constitute the variety of notes for that new piece of music which his life is.”
—Ralph Waldo Emerson (1803–1882)