# ag.algebraic geometry – Extension of a holomorphic vector bundle on a nodal curve

I am reading a paper on holomorphic curves and stuck in an argument about extension of a given holomorphic vector bundle over a nodal curve.

Let $$C$$ be a nodal curve without closed componets and $$E$$ a holomorphic vector bundle on $$C$$. For a compact nodal curve $$tilde{C}$$ containing $$C$$, how can $$E$$ extend to a holomorphic vector bundle $$tilde{E}$$ on $$tilde{C}$$? Moreover, in the same paper, the author claims that one can choose $$tilde{E}$$ in such a way that $$langle c_{1}(tilde{E}), tilde{C}_{i} rangle$$ is sufficiently large for any component $$tilde{C}_{i} subset tilde{C}$$. Could you please tell me how to take such an extension?

Any hint and comment are really appreciated. Thank you in advance.