  We study the rational Picard group of the projectivized moduli space of
holomorphic n-differentials on complex genus g stable curves. We define (n - 1)
natural classes in this Picard group that we call Prym-Tyurin classes. We
express these classes as linear combinations of boundary divisors and the
divisor of n-differentials with a double zero. We give two different proofs of
this result, using two alternative approaches: an analytic approach that
involves the Bergman tau function and its vanishing divisor and an
algebro-geometric approach that involves cohomological computations on the
universal curve.
