Extending vector bundles on curves

Given a curve in a (smooth) projective variety $C \subset X$ over an algebraically closed field $k$, we show that a vector bundle $V$ on $C$ can be extended to a ($\mu$-stable) vector bundle on $X$ if rank$(V) \geq \dim(X)$ and $\operatorname{det}(V)$ extends to $X$.

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This research was conducted in the framework of the research training group GRK 2240: Algebro-geometric Methods in Algebra, Arithmetic and Topology, which is funded by the Deutsche Forschungsgemeinschaft.

Received 16 October 2020

Accepted 4 April 2021

Published 21 April 2023