Splitting criteria for vector bundles on higher-dimensional varieties (Q650119)

The author studies criteria for smooth complex projective varieties so that a vector bundle splits as a direct sum of line bundles if its restriction to an ample section splits. The techniques are modifications of the corresponding theorem by \textit{G.~Horrocks} [Proc. Lond. Math. Soc., III. Ser. 14, 689--713 (1964; Zbl 0126.16801)] and Grothendieck-Lefschetz Theorem.