Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree

Details Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree

2010-05-21

arxiv.org/abs/1005.3988v1

Mathematische Zeitschrift, Volume 265, Number 3 / July, 2010 pages 493-509

Mathematics

Algebraic Geometry

15 pages

Scientific paper

10.1007/s00209-009-0526-7

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.

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