Communications of the
Korean Mathematical Society CKMS

We extend the work of A. Beauville on rank $2$ vector bundles on a smooth curve in several directions. We give families of examples with large dimension, add new existence and non-existence results and prove the existence of indecomposable limits with arbitrary rank. To construct the large dimensional families we use the examples of limits of rank $2$ trivial bundles on $\mathbb {P}^2$ and $\mathbb {P}^3$ due to C. Banica. We also consider a more flexible notion: limits of trivial bundles on nearby curves.

Keywords: Vector bundle, rank $2$ vector bundle, vector bundles on curves, degenerations of a vector bundle, limits of trivial bundles

MSC numbers: Primary 14H60, 14J60, 14H51