THE BOUNDARY OF THE p-RANK 0 STRATUM OF THE MODULI SPACE OF CYCLIC COVERS OF THE PROJECTIVE LINE

We study the p-rank stratification of the moduli space of cyclic degree l covers of the projective line in characteristic p for distinct primes p and l. The main result is about the intersection of the p-rank 0 stratum with the boundary of the moduli space of curves. When l = 3 and p 2 mod 3 is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p, for every genus g, signature type (r, s), and p-rank f satisfying the clear necessary conditions.