Let $C$ be smooth curve, and let $F$ be a stable rank 2 vector bundle of odd degree equal $2c+1$, and fix a point $p\in C$:

Can one choose an epi-morphism $u:F\rightarrow \mathbb C_p$ such that $u$ does not vanish on all the sub-line bundle of $F$ of degree $c$? (where $\mathbb C_p$ is the skyscraper sheaf)

Thank you.

Let $C$ be smooth curve, and let $F$ be a stable rank 2 vector bundle of degree equal to $2c+1$, $c\in\mathbb{N}$, and fix a point $p\in C$:

Can one choose an epi-morphism $u:F\rightarrow \mathbb C_p$ such that $u$ does not vanish on all the sub-line bundles of $F$ of degree $c$? (where $\mathbb C_p$ is the skyscraper sheaf)

Thank you.

Let $C$ be smooth curve, and let $F$ be a stable rank 2 vector bundle of odd degree equal $2c+1$, and fix a point $p\in C$:

Can one choose an epi-morphism $u:F\rightarrow \mathbb C_p$ such that $u$ does not vanish on all the sub-line bundle of $F$ of degree $c$?

Thank you.

Let $C$ be smooth curve, and let $F$ be a stable rank 2 vector bundle of odd degree equal $2c+1$, and fix a point $p\in C$:

Can one choose an epi-morphism $u:F\rightarrow \mathbb C_p$ such that $u$ does not vanish on all the sub-line bundle of $F$ of degree $c$? (where $\mathbb C_p$ is the skyscraper sheaf)

Thank you.