Line bundles for which a projectivized jet bundle is a product
HTML articles powered by AMS MathViewer
- by Sandra Di Rocco and Andrew J. Sommese
- Proc. Amer. Math. Soc. 129 (2001), 1659-1663
- DOI: https://doi.org/10.1090/S0002-9939-00-05875-5
- Published electronically: December 13, 2000
- PDF | Request permission
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
- Mauro C. Beltrametti and Andrew J. Sommese, The adjunction theory of complex projective varieties, De Gruyter Expositions in Mathematics, vol. 16, Walter de Gruyter & Co., Berlin, 1995. MR 1318687, DOI 10.1515/9783110871746
- Phillip Griffiths and Joseph Harris, Algebraic geometry and local differential geometry, Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 3, 355–452. MR 559347
- Antonio Kumpera and Donald Spencer, Lie equations. Vol. I: General theory, Annals of Mathematics Studies, No. 73, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0380908
- Robert Lazarsfeld, Some applications of the theory of positive vector bundles, Complete intersections (Acireale, 1983) Lecture Notes in Math., vol. 1092, Springer, Berlin, 1984, pp. 29–61. MR 775876, DOI 10.1007/BFb0099356
- Andrew John Sommese, Compact complex manifolds possessing a line bundle with a trivial jet bundle, Abh. Math. Sem. Univ. Hamburg 47 (1978), 79–91. MR 499332, DOI 10.1007/BF02941353
Bibliographic Information
- Sandra Di Rocco
- Affiliation: Department of Mathematics, KTH, Royal Institute of Technology, S-100 44 Stockholm, Sweden
- MR Author ID: 606949
- Email: sandra@math.kth.se
- Andrew J. Sommese
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- Email: sommese@nd.edu
- Received by editor(s): June 30, 1998
- Received by editor(s) in revised form: October 13, 1999
- Published electronically: 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 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1659-1663
- MSC (2000): Primary 14J40, 14M99
- DOI: https://doi.org/10.1090/S0002-9939-00-05875-5
- MathSciNet review: 1814094