Splitting of Low-Rank ACM Bundles on Hypersurfaces of High Dimension

Abstract

Let X be a smooth projective hypersurface. We derive a splitting criterion for arithmetically Cohen–Macaulay bundles over X. As an application, we show that any rank 3 ACM vector bundle over X splits when dim X ≥ 7. We also derive a splitting result for rank 4 arithmetically Cohen–Macaulay bundles.

Key Words:

• Arithmetically Cohen–Macaulay
• Hypersurfaces
• Vector bundles

2010 Mathematics Subject Classification:

• 14J60

ACKNOWLEDGMENT

We thank Suresh Nayak for outlining a proof for the ∧ −Sym and Sym − ∧ sequences. We thank Jishnu Biswas and G. V. Ravindra for providing support and motivation. We thank the referee for various feedbacks in improving the exposition.

Notes

¹We were unable to find any standard terminology in the literature for the given resolution.