Existence of Indecomposable Rank Two Vector Bundles on Higher Dimensional Toric Varieties

摘要

In the mid 1970s, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on ?~n is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain ?~n.