Geodesic
Some Adjunction Properties of Ample Vector Bundles
Canadian mathematical bulletin, Tome 44 (2001) no. 4, pp. 452-458

Voir la notice de l'article provenant de la source Cambridge University Press

Let $\mathcal{E}$ be an ample vector bundle of rank $r$ on a projective variety $X$ with only log-terminal singularities. We consider the nefness of adjoint divisors ${{K}_{X}}\,+\,\left( t-r \right)\,\det \,\mathcal{E}$ when $t\,\ge \,\dim\,X$ and $t\,>\,r$ . As an application, we classify pairs $\left( X,\,\mathcal{E} \right)$ with ${{c}_{r}}$ -sectional genus zero.
DOI : 10.4153/CMB-2001-045-7
Mots-clés : 14J60, 14C20, 14F05, 14J40, ample vector bundle, adjunction, sectional genus 
Ishihara, Hironobu. Some Adjunction Properties of Ample Vector Bundles. Canadian mathematical bulletin, Tome 44 (2001) no. 4, pp. 452-458. doi: 10.4153/CMB-2001-045-7
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[A] [A] Andreatta, M., Some remarks on the study of good contractions. Manuscripta Math. 87 (1995), 359–367. Google Scholar

[AW] [AW] Andreatta, M. and Wísniewski, J. A., A note on nonvanishing and applications. Duke Math. J. 72 (1993), 739–755. Google Scholar

[Ba] [Ba] Ballico, E., On vector bundles on 3-folds with sectional genus 1. Trans. Amer.Math. Soc. 324 (1991), 135–147. Google Scholar

[BS] [BS] Beltrametti, M. C. and Sommese, A. J., The Adjunction Theory of Complex Projective Varieties. In: Expositions in Math. 16, de Gruyter, 1995. Google Scholar

[F0] [F0] Fujita, T., Classification Theories of Polarized Varieties. LondonMath. Soc. Lecture Note Ser. 155, Cambridge University Press, 1990. Google Scholar

[F1] [F1] Fujita, T., On the structure of polarized varieties with Δ-genera zero. J. Fac. Sci. Univ. Tokyo 22 (1975), 103–115. Google Scholar

[F2] [F2] Fujita, T., Remarks on quasi-polarized varieties. Nagoya Math. J. 115 (1989), 105–123. Google Scholar

[FuI] [FuI] Fukuma, Y. and Ishihara, H., A generalization of curve genus for ample vector bundles, II. Pacific J. Math. 193 (2000), 307–326. Google Scholar

[I] [I] Ishihara, H., A generalization of curve genus for ample vector bundles, I. Comm. Algebra 27 (1999), 4327–4335. Google Scholar

[K] [K] Kawamata, Y., On the length of an extremal rational curve. Invent.Math. 105 (1991), 609–611. Google Scholar

[LM] [LM] Lanteri, A. and Maeda, H., Ample vector bundles of curve genus one. Canad. Math. Bull. 42 (1999), 209–213. Google Scholar

[LMS] [LMS] Lanteri, A., Maeda, H. and Sommese, A. J., Ample and spanned vector bundles of minimal curve genus. Arch. Math. (Basel) 66 (1996), 141–149. Google Scholar

[M1] [M1] Maeda, H., Ramification divisors for branched coverings of P . Math. Ann. 288 (1990), 195–199. Google Scholar

[M2] [M2] Maeda, H., Ample vector bundles of small curve genera. Arch. Math. (Basel) 70 (1998), 239–243. Google Scholar

[Me] [Me] Mella, M., Vector bundles on log terminal varieties. Proc. Amer.Math. Soc. 126 (1998), 2199–2204. Google Scholar

[YZ] [YZ] Ye, Y. G. and Zhang, Q., On ample vector bundles whose adjunction bundles are not numerically effective. Duke Math. J. 60 (1990), 671–687. Google Scholar

[Z1] [Z1] Zhang, Q., Ample vector bundles on singular varieties. Math. Z. 220 (1995), 59–64. Google Scholar

[Z2] [Z2] Zhang, Q., Ample vector bundles on singular varieties II. Math. Ann. 307 (1997), 505–509. Google Scholar

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