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Original Articles

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

Pages 1011-1017 | Received 30 Mar 2013, Published online: 25 Jan 2016

REFERENCES

  • Atiyah, M. F. (1956). On the Krull-Schmidt theorem with application to sheaves. Bulletin de la S. M. F. 84:307–317.
  • Buchweitz, R.-O., Greuel, G.-M., Schreyer, F.-O. (1987). Cohen-Macaulay modules on hypersurface singularities II. Inv. Math. 88:165–182.
  • Casanellas, M., Hartshorne, R. (2011). ACM bundles on cubic surfaces. J. Eur. Math. Soc. 13:709–731.
  • Chiantini, L., Madonna, C. (2002). ACM bundles on a general quintic threefold. Matematiche (Catania) 55(2000)(2):239–258.
  • Chiantini, L., Madonna, C. (2004). A splitting criterion for rank 2 bundles on a general sextic threefold. Internat. J. Math. 15(4):341–359.
  • Chiantini, L., Madonna, C. (2005). ACM bundles on a general hypersurfaces in ℙ5 of low degree. Collect. Math. 56(1):85–96.
  • Deligne, P., Katz, N. (1973). Séminaire de Géométrie Algébrique du Bois-Marie - 1967-1969. Groupes de monodromie en géométrie algébrique. II. LNM, Vol. 340. Springer-Verlag.
  • Eisenbud, D. (1995). Commutative Algebra with a View toward Algebraic Geometry. Springer-Verlag.
  • Hartshorne, R. (1970). Ample Subvarieties of Algebraic Varieties. LNM, Vol. 156. Springer-Verlag.
  • Horrocks, G. (1964). Vector bundles on the punctured spectrum of a local ring. Proc. London Math. Soc. 14:689–713.
  • Fujita, T. (1981). Vector bundles on ample divisors. J. Math. Soc. Japan 33(3):405–414.
  • Kleiman, S. L. (1969). Geometry on grassmannians and applications to splitting bundles and smoothing cycles. Publ. Math. IHES 36(1):281–297.
  • Kleppe, H. (1978). Deformation of schemes defined by vanishing of pfaffians. Jour. of Algebra 53:84–92.
  • Knörrer, H. (1987). Cohen-Macaulay modules on hypersurface singularities I. Inv. Math. 88:153–164.
  • Mohan Kumar, N., Rao, A. P., Ravindra, G. V. (2007). Arithmetically Cohen-Macaulay bundles on hypersurfaces. Commentarii Mathematici Helvetici 82(4):829–843.
  • Mohan Kumar, N., Rao, A. P., Ravindra, G. V. (2007). Arithmetically Cohen-Macaulay bundles on three dimensional hypersurfaces. Int. Math. Res. Not. IMRN, No. 8, Art. ID rnm025, 11pp.
  • Mohan Kumar, N., Rao, A. P., Ravindra, G. V. On codimension two subvarieties in hypersurfaces. In: de Jeu, R. Lewis, J. eds. Motives and Algebraic Cycles: A Celebration in honour of Spencer Bloch, Fields Institute Communications. Vol. 56, pp. 167–174.
  • Ravindra, G. V. (2009). Curves on threefolds and a conjecture of Griffiths-Harris. Math. Ann. 345:731–748.
  • Tadakazu, S. (2010). A sufficient condition for splitting of arithmetically Cohen-Macaulay bundles on general hypersurfaces. Comm. Algebra 38(5):1633–1639.
  • Weyman, J. M. (2003). Cohomology of Vector Bundles and Syzygies. Cambridge Tracts in Mathematics, Vol. 149.

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