|Location:||MSRI: Simons Auditorium|
In a pair of Invenitones papers in 1995 and 1998, Borcherds gave a construction of meromorphic modular forms on the hermitian symmetric domain associated to a rational quadratic space V, ( , ) of signature (n,2). These modular forms have remarkable properties including
(1) an explicit divisor given in terms of special divisors and
(2) product formulas, each valid in a neighborhood of a point boundary component.
In this lecture, after reviewing Borcherds' construction, and under the assumption that V, ( , ) admits 2-dimensional rational isotropic subspaces, I will describe some new product formulas for these modular forms, each valid in the neighborhood of a 1-dimensional boundary component. The products involve Jacobi theta functions and eta functions.
They should prove useful in understanding the integral theory of Borcherds forms.