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

Here we consider the set of bundles {V_n}_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 V_n is a function of the congruence class of p modulo 2λ_h (an integer invariant associated to h). As one of the consequences of this, we prove that if V_n is semistable in char 0 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 V_n, there is a common Zariski dense set of such primes.