Stable vector bundles on curves: numerical invariants of their extremal subbundles

Abstract

Let $X$ be a smooth projective curve of genus $g \geq 2$ and $E$ a rank $r$ vector bundle on $X$. If $1 \leq t < r$ set $s_t(E)$:= sup $\lbrace t$(deg($E$)) - $r$(deg($F$)), where $F$ is a rank $t$ subsheaf of $E \rbrace $. Here we construct rank $r$ stable vector bundles $E$ on $X$ such that the sequence $ \lbrace s_t(E) \rbrace _{1 \leq t<r}$ has a prescribed value and the set of all subsheaves of $E$ with maximal degree may be explicitely described.