|Given a moduli space, what is the "best" effective divisor
one can construct on it? We present a very general method of
constructing divisors on moduli spaces using the syzygies of the
objects. Applications of this method include:
(1) a proof that the moduli space of curves of genus 22 is of general type, and
(2) a proof that the moduli space S_g of curves of genus g together with an even theta-characteristic is of general type for g > 8.