Limits of trivial bundles on curves
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 43-61
Published online January 31, 2020
Edoardo Ballico
University of Trento
Abstract : 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
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