Maximal Subbundles 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 $E_*\in M(r,d)$ and a subbundle $F\, \subset\, E$ of rank $r'$ and fixed induced parabolic structure, set $s^{par}(E_*,F_*)\, :=\, dr'-\text{deg}(F)r$, 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 $s^{par}(E_*,F_*)$ taken over all such subbundles $F$. We investigate the strata of $M(r,d)$ defined by values of $s^{par}_{r'}(E_*)$.