Arithmetic behaviour of Frobenius semistability of syzygy bundles for plane trinomial curves

Here we consider the set of bundles {Vn}n∈N associated to the plane trinomial curves k[x,y,z]/(h). We prove that the Frobenius semistability behaviour of the reduction mod p of Vn is a function of the congruence class of p modulo 2λh (an integer invariant associated to h).As one of the consequences of this, we prove that if Vn is semistable in char0 then its reduction mod p is strongly semistable, for p in a Zariski dense set of primes. Moreover, for any given finitely many such semistable bundles Vn, there is a common Zariski dense set of such primes.