A proof of the Trisecant Identity through the Fourier-Mukai transform

TL;DR

This paper uses the Fourier-Mukai transform to explicitly generate the ideal defining an algebraic curve within its Jacobian, linking it to Fay's trisecant identities.

Contribution

It provides a new explicit method to generate the ideal of a curve in its Jacobian using Fourier-Mukai transform, connecting to classical trisecant identities.

Findings

Explicit generators for the ideal of a curve in its Jacobian

Connection established between Fourier-Mukai transform and Fay's trisecant identities

Enhanced understanding of algebraic curve embeddings

Abstract

Using the technique of the Fourier-Mukai transform we give an explicit set of generators of the ideal defining an algebraic curve as a subscheme of its Jacobian. Essentially, these ideals are generated by the Fay's trisecant identities.