Fay's trisecant identity

In algebraic geometry, '''Fay's trisecant identity''' is an identity between theta functions of Riemann surfaces introduced by . Fay's identity holds for theta functions of Jacobians of curves, but not for theta functions of general abelian varieties.

The name "trisecant identity" refers to the geometric interpretation given by , who used it to show that the Kummer variety of a genus ''g'' Riemann surface, given by the image of the map from the Jacobian to projective space of dimension $2^g-1$ induced by theta functions of order 2, has a 4-dimensional space of trisecants. Provided by Wikipedia