HONOURS TALK

Speaker: Kenneth Chan (UNSW)

Title: The Jacobian variety and the Torelli theorem
Date: Fiday 22nd October 2004
Time: 2:00 pm
Venue: RC-4082, The Red Centre, UNSW

In the study of compact Riemann surfaces, the Jacobian variety plays an important
role. To each Riemann surface, S, one can associate to S a topological genus g. The Jacobian variety is the quotient space \mathbb{C}^g/\Lambda, where \Lambda is the \mathbb{Z} linear span of the periods of S.

In the talk, we shall see more precisely what this means, and how the Jacobian arises naturally.
The Torelli theorem states that given a Jacobian variety, as well as an additional piece of data called the principal polarisation,the compact Rieman surface is determined up to isomorphism.

This assures us that in studying a Riemann
surface using via its Jacobian variety, no information is lost. In the talk, we will see a few highlights of its proof, which uses techniques in algebraic geometry.