When every Vector Bundle is a Direct Sum of Line Bundles?

摘要

Here we prove the following result. Let X be a reducedand connected projective variety. Every vector bundle on X isisomorphic to a direct sum of line bundles if and only if everyirreducible component of X is isomorphic to P1, every singularpoint of X is an ordinary node and every irreducible componentof X contains at most two singular points of X.