Existence of Rank Two Vector Bundles on Higher Dimensional Toric Varieties
Abstract
In the mid 70's, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on Pn 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 Pn
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