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 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)
“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)