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Transactions of the American Mathematical Society
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On the adjunction mapping of very ample vector bundles of corank one

Author(s): Antonio Lanteri; Marino Palleschi; Andrew J. Sommese
Journal: Trans. Amer. Math. Soc. 356 (2004), 2307-2324.
MSC (2000): Primary 14F05, 14N30, 14C20; Secondary 14J40
Posted: October 6, 2003
MathSciNet review: 2048519
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Abstract: Let $\mathcal{E}$ be a very ample vector bundle of rank $n-1$ over a smooth complex projective variety $X$ of dimension $n\geq 3$. The structure of $(X,\mathcal{E})$ being known when $\kappa (K_{X} + \det \mathcal{E}) \leq 0$, we investigate the structure of the adjunction mapping when $0 < \kappa (K_{X} + \det \mathcal{E}) < n$.

References:

[ABW]
M. Andreatta, E. Ballico, and J. A. Wisniewski, Vector bundles and adjunction, Internat. J. Math. 3 (1992), 331-340. MR 93h:14031

[BS1]
M. C. Beltrametti and A. J. Sommese, Comparing the classical and the adjunction theoretic definition of scrolls, Geometry of Complex Projective Varieties (A. Lanteri, M. Palleschi, and D. Struppa, eds.), Proc. Cetraro 1990, Mediterranean, Rende, 1993, pp. 55-74. MR 94e:14053

[BS2]
-, The Adjunction Theory of Complex Projective Varieties, Expositions in Mathematics, vol. 16, De Gruyter, Berlin - New York, 1995. MR 96f:14004

[BS3]
-, On the dimension of the adjoint linear system for threefolds, Ann. Sc. Norm. Sup. Pisa, IV 22 (1995), 1-24. MR 96e:14005

[Bo]
F. Bogomolov, Holomorphic tensors and vector bundles on projective varieties, Math. USSR Isvestija 13 (1979), 499-555.

[Fu]
W. Fulton, Intersection Theory, Ergebnisse der Math., vol. 2, Springer, 1984. MR 85k:14004

[Ha]
R. Hartshorne, Ample vector bundles on curves, Nagoya Math. J. 43 (1971), 73-89. MR 45:1929

[I1]
P. Ionescu, Embedded projective varieties of small invariants, Algebraic Geometry (L. Badescu et al., eds.), Proc. Bucharest 1982, Springer, Berlin, 1984, pp. 142-186. MR 85m:14024

[I2]
-, Embedded projective varieties of small invariants, III, Algebraic Geometry (A. J. Sommese, A. Biancofiore, and E. L. Livorni, eds.), Proc. L'Aquila 1988, Springer, Berlin, Heidelberg, 1990, pp. 138-154. MR 91e:14014

[LM]
A. Lanteri and H. Maeda, Ample vector bundle characterizations of projective bundles and quadric fibrations over curves, Higher Dimensional Complex Varieties (M. Andreatta and Th. Peternell, eds.), Proc. Trento 1994, De Gruyter, Berlin, New York, 1996, pp. 247-259. MR 98h:14051

[LMS]
A. Lanteri, H. Maeda, and A. J. Sommese, Ample and spanned vector bundles of minimal curve genus, Arch. Math. 66 (1996), 141-149. MR 96k:14034

[LP]
A. Lanteri and M. Palleschi, About the adjunction process for polarized algebraic surfaces, J. reine angew. Math. 352 (1984), 15-23. MR 86h:14028

[MS]
H. Maeda and A. J. Sommese, Very ample vector bundles of curve genus two, Arch. Math. 79 (2002), 74-80. MR 2003f:14062

[Mo]
S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176. MR 84e:14032

[OSS]
Ch. Okonek, M. Schneider, H. Spindler, Vector Bundles on Complex Projective Spaces, Progr. Math., vol. 3, Birkhäuser, Boston, 1980. MR 81b:14001

[PSW]
Th. Peternell, M. Szurek, and J. A. Wisniewski, Fano manifolds and vector bundles, Math. Ann. 249 (1992), 151-165. MR 93h:14030

[R]
M. Reid, Bogomolov's theorem $c_{1}^{2} \leq 4c_{2}$, Proc. Internat. Symposium on Alg. Geom., Kyoto, 1977, pp. 623-642. MR 82b:14014

[Re]
I. Reider, Vector bundles of rank $2$ and linear systems on algebraic surfaces, Ann. of Math. 127 (1988), 309-316. MR 89e:14038

[S]
A. J. Sommese, Submanifolds of abelian varieties, Math. Ann. 233 (1978), 229-256. MR 57:6524

[SV]
A. J. Sommese and A. Van de Ven, On the adjunction mapping, Math. Ann. 278 (1987), 593-603. MR 88j:14011

[SW]
M. Szurek and J. A. Wisniewski, Fano bundles of rank $2$ on surfaces, Compositio Math. 76 (1990), 295-305. MR 92e:14037

[YZ]
Y.-G. Ye and Q. Zhang, On ample vector bundles whose adjunction bundles are not numerically effective, Duke Math. J. 60 (1990), 671-687. MR 91g:14040

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Additional Information:

Antonio Lanteri
Affiliation: Dipartimento di Matematica ``F. Enriques'', Università, Via C. Saldini 50, I-20133 Milano, Italy
Email: lanteri@mat.unimi.it

Marino Palleschi
Affiliation: Dipartimento di Matematica ``F. Enriques'', Università, Via C. Saldini 50, I-20133 Milano, Italy
Email: palleschi@mat.unimi.it

Andrew J. Sommese
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556-4618
Email: sommese@nd.edu

DOI: 10.1090/S0002-9947-03-03278-1
PII: S 0002-9947(03)03278-1
Keywords: Vector bundle (very ample), adjunction mapping
Received by editor(s): July 10, 2001
Received by editor(s) in revised form: October 22, 2002
Posted: October 6, 2003
Dedicated: To the memory of Meeyoung Kim
Copyright of article: Copyright 2003, American Mathematical Society




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