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.
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“The virtue of art lies in detachment, in sequestering one object from the embarrassing variety. Until one thing comes out from the connection of things, there can be enjoyment, contemplation, but no thought.”
—Ralph Waldo Emerson (1803–1882)
“To invent without scruple a new principle to every new phenomenon, instead of adapting it to the old; to overload our hypothesis with a variety of this kind, are certain proofs that none of these principles is the just one, and that we only desire, by a number of falsehoods, to cover our ignorance of the truth.”
—David Hume (1711–1776)