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Line bundles for which a projectivized jet bundle is a product

Author(s): Sandra Di Rocco; Andrew J. Sommese
Journal: Proc. Amer. Math. Soc. 129 (2001), 1659-1663.
MSC (2000): Primary 14J40, 14M99
Posted: December 13, 2000
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Abstract: We characterize the triples $(X,L,H)$, consisting of line bundles $L$ and $H$ on a complex projective manifold $X$, such that for some positive integer $k$, the $k$-th holomorphic jet bundle of $L$, $J_k(X,L)$, is isomorphic to a direct sum $H\oplus\dots\oplus H$.

References:

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M.C. Beltrametti and A.J. Sommese, The Adjunction Theory of Complex Projective Varieties, Expositions in Math. 16 (1995), W. de Gruyter, Berlin. MR 96f:14004
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P. Griffiths and J. Harris, Algebraic geometry and local differential geometry, Ann. Sci. Ècole Norm. Sup. (4) 12 (1979), 355-432.MR 81k:53004

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A. Kumpera and D. Spencer, Lie Equations; Vol. I: General Theory, Ann. of Math. Stud. 73 (1972), Princeton University Press, Princeton, N.J.MR 52:1805

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R. Lazarsfeld, Some applications of the theory of positive vector bundles, Complete Intersections, CIME course 1983, Acireale (Catania) ed. by S. Greco and R. Strano, Lecture Notes in Math. 1092 (1984), 29-61, Springer-Verlag, New York.MR 86d:14013

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A.J. Sommese, Compact Complex Manifolds possessing a line bundle with a trivial jet bundle, Abh. Math. Sem. Univ. Hamburg 47 (1978), 79-91. MR 58:17231

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Additional Information:

Sandra Di Rocco
Affiliation: Department of Mathematics, KTH, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Email: sandra@math.kth.se

Andrew J. Sommese
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: sommese@nd.edu

DOI: 10.1090/S0002-9939-00-05875-5
PII: S 0002-9939(00)05875-5
Keywords: Jet bundle, complex projective manifold, projective space, Abelian variety
Received by editor(s): June 30, 1998
Received by editor(s) in revised form: October 13, 1999
Posted: December 13, 2000
Additional Notes: The first author would like to thank the Max Planck Institute for its support.
The second author would like to thank the Max Planck Institute and the Alexander von Humboldt Foundation for its support.
Communicated by: Ron Donagi
Copyright of article: Copyright 2000, American Mathematical Society

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