Parabolic Raynaud bundles

Abstract

Let X be an irreducible smooth projective curve defined over the field of complex numbers, $S=\{p_1, p_2,\ldots,p_n\} \subset X$ a finite set of closed points and N ≥ 2 a fixed integer. For any pair $(r,d)\in {\mathbb N} \times \frac{1}{N} {\mathbb Z}$, there exists a parabolic vector bundle $R_{r,d,*}$ on X, with parabolic structure over S and all parabolic weights in $\frac{1}{N} \mathbb Z$, that has the following property: Take any parabolic vector bundle $E_*$ of rank r on X whose parabolic points are contained in S, all the parabolic weights are in $\frac{1}{N}\mathbb Z$ and the parabolic degree is d. Then $E_*$ is parabolically semistable if and only if there is no nonzero parabolic homomorphism from $R_{r,d,*}$ to $E_*$.