Maximal subsheaves of parabolic vector bundles

Abstract

Let X be a complex irreducible smooth projective curve of genus at least two and M(r, d) a moduli space of stable parabolic vector bundles over X of rank r and degree d with a fixed parabolic structure. For any parabolic bundle E∗ ∈ 2 M(r, d) and a subbundle F ⊂ E of rank r′ and fixed induced parabolic structure, set s^par(E∗, F∗) := dr′ − deg(F)r, where F∗ is F equipped with the induced parabolic structure. If E∗ has a subbundle of rank r′ with the fixed induced parabolic structure, then let s^par_r' (E∗) be the minimum of spar(E∗, F∗) taken over all such subbundles F. We investigate the strata of M(r, d) defined by values of s^par_r' (E∗).