Resumen de Decomposable subbundles of polystable vector bundles on projective curves

Edoardo Ballico

• Let $X$ be a smooth projective curve of genus $g\geq 4$. Here we show the existence for several numerical invariants $x> 0$, deg($E_i$), rank($E_i$), $1 \leq i \leq x$, deg($F$), rank($F$) of semistable vector bundles $E_i, 1\leq i\leq x, F$ on $X$ such that $E :=\oplus_{1\leq i\leq x}E_i$ is a saturated subbundle of $F$ and $F/E$ is semistable. If $X$ is either bielliptic or with general moduli we may find stable vector bundles $E_i, 1\leq i\leq x$, and $F$ with $F/E$ stable.