A remark on stability and restrictions of vector bundles to hypersurfaces
In the abundant literature on the stability of vector bundles, the relation between the stability of a bundle and the stability of its restriction to a subvariety has often been considered. This paper adds to the body of work by showing that a vector bundle on a smooth algebraic variety \(X\) with \(\dim(X)\geq 2\) is slope (semi-)stable with respect to an ample divisor \(H\) if its restriction to any smooth ample divisor \(Y\) equivalent to \(mH\) is slope (semi-)stable with respect to \(H\vert_Y\).
scientific article; zbMATH DE number 7342843
scientific article