Existence of Rank Two Vector Bundles on Higher Dimensional Toric Varieties

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

2010-05-30

arxiv.org/abs/1005.5546v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

In the mid 70's, Hartshorne conjectured that, for all n > 7, any rank 2
vector bundles on P^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 P^n

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