Jacobian Variety - Introduction

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:

    My objection to Liberalism is this—that it is the introduction into the practical business of life of the highest kind—namely, politics—of philosophical ideas instead of political principles.
    Benjamin Disraeli (1804–1881)

    The role of the stepmother is the most difficult of all, because you can’t ever just be. You’re constantly being tested—by the children, the neighbors, your husband, the relatives, old friends who knew the children’s parents in their first marriage, and by yourself.
    —Anonymous Stepparent. Making It as a Stepparent, by Claire Berman, introduction (1980, repr. 1986)

    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.)