Construction of the Moduli Space of Vector Bundles on an Orbifold Curve

Let k be an algebraically closed field of any characteristic, and let (X, P) be an orbifold curve over k. We construct the moduli space M (ₗ, ₏) ^ss (n, ) of P-semistable bundles on (X, P) of rank n and determinant. In the characteristic zero case, this result is well known and follows from GIT techniques. Our construction follows a different approach inspired by a GIT-free construction of Faltings. We show that when the moduli space is non-empty, it is a finite disjoint union of irreducible projective varieties.