Extending Vector Bundles from Curves

Abstract

Given a curve in a (smooth) projective variety $C\subset X$, we show that a vector bundle $V$ on C can be extended to a ($\mu$-stable) vector bundle on $X$ if $\text{rank}(V)\ge \text{dim}(X)$ and $\text{det}(V)$ extends to $X$.

arXiv commentSection 2 completely rewritten, to appear in Mathematical Research Letters