Mathematics

The Jacobian varieties of smooth projective curves fit together to form a family over the moduli space of curves called universal Jacobian, and the theta divisors of these curves form a divisor in the universal Jacobian.  I will explain how to construct extensions of the universal Jacobian and theta divisor over the moduli space of stable curves. The extensions depend on an extra stability parameter, and I will then study how the universal theta divisor varies with this parameter. This is a joint work with Jesse Kass.