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- Publisher
- de Gruyter
- Copyright
- Copyright © 2003 by Walter de Gruyter GmbH & Co. KG
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/form.2003.029
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. Let X be a smooth complex projective manifold and let Z be a smooth submanifold of dimension b 2, which is the zero locus of a section of an ample vector bundle E of rank n À dim Z b 2 on X. Let H be an ample line bundle on X whose restriction HZ to Z is very ample. Triplets ðX ; E; HÞ as above are classified under the assumption that the polarized manifold ðZ; HZ Þ admits a hyperelliptic curve section. 1991 Mathematics Subject Classification: 14F05, 14J60, 14N30; 14C20, 14J26. Introduction and statement of the result The study of projective manifolds admitting a hyperelliptic curve among their linear sections has a long history, concluded by the complete understanding of the adjunction mapping for a very ample line bundle ([SV], [Se]). In recent years several results known in the framework of hyperplane sections have been extended to the more general setting of ample or very ample vector bundles. Trying to do that for the theme of hyperelliptic curve sections is very dicult due to the lack of information about the refined properties of the adjunction mapping in this general setting. For results in this direction
Journal
Forum Mathematicum – de Gruyter
Published: May 21, 2003