Introduction
The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension g, and hence, over the complex numbers, it is a complex torus. If p is a point of C, then the curve C can be mapped to a subvariety of J with the given point p mapping to the identity of J, and C generates J as a group.
Read more about this topic: Jacobian Variety
Famous quotes containing the word introduction:
“For the introduction of a new kind of music must be shunned as imperiling the whole state; since styles of music are never disturbed without affecting the most important political institutions.”
—Plato (c. 427–347 B.C.)
“Such is oftenest the young man’s introduction to the forest, and the most original part of himself. He goes thither at first as a hunter and fisher, until at last, if he has the seeds of a better life in him, he distinguishes his proper objects, as a poet or naturalist it may be, and leaves the gun and fish-pole behind. The mass of men are still and always young in this respect.”
—Henry David Thoreau (1817–1862)
“For better or worse, stepparenting is self-conscious parenting. You’re damned if you do, and damned if you don’t.”
—Anonymous Parent. Making It as a Stepparent, by Claire Berman, introduction (1980, repr. 1986)