### Abstract

This the original TeX file for my article Jacobian Varieties, published as
Chapter VII of Arithmetic geometry (Storrs, Conn., 1984), 167--212, Springer,
New York, 1986. The table of contents has been restored, some corrections and
minor improvements to the exposition have been made, and an index has been
added. The numbering is unchanged.

The article contains a detailed treatment of Jacobian varieties.
Sections 2, 5, and 6 prove the basic properties of Jacobian varieties starting
from the definition in Section 1, while the construction of the Jacobian is
carried out in Sections 3 and 4. The remaining sections are largely
independent of one another.

### Contents

- Definitions
- The canonical maps from
*C* to its Jacobian variety
- The symmetric powers of a curve
- The construction of the Jacobian variety
- The canonical maps from the symmetric powers of
*C* to its Jacobian variety
- The Jacobian variety as Albanese variety; autoduality
- Weil's construction of the Jacobian variety
- Generalizations
- Obtaining coverings of curve from its Jacobian
- Abelian varieties are quotients of Jacobian varieties
- The zeta function of curve
- Torelli's theorem: statement and applications
- Torelli's theorem: the proof
- Bibliographic notes for "Abelian Varieties" and "Jacobian Varieties"

pdf (first posted 12.08.12, 43 pages).