Mathematische Zeitschrift

, Volume 265, Issue 3, pp 493–509 | Cite as

Arithmetically Cohen–Macaulay bundles on complete intersection varieties of sufficiently high multidegree

  • Jishnu Biswas
  • G. V. RavindraEmail author


Recently it has been proved that any arithmetically Cohen–Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.


Exact Sequence Vector Bundle Line Bundle Complete Intersection Chern Class 
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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Theoretical Statistics and Mathematics UnitIndian Statistical InstituteBangaloreIndia
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  3. 3.Department of Mathematics and Computer ScienceUniversity of MissouriSt. LouisUSA

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