Notes on very ample vector bundles on 3-folds
Let be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of is provided when is nef but not big, and when a suitable positive multiple of defines a morphism X → B with connected fibers onto a smooth projective curve B, where...
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| Veröffentlicht in: | Archiv der Mathematik 2005-12, Vol.85 (6), p.527-537 |
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| container_title | Archiv der Mathematik |
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| creator | Maeda, Hidetoshi Sommese, Andrew J. |
| description | Let be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of is provided when is nef but not big, and when a suitable positive multiple of defines a morphism X → B with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus of B is positive and has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result is improved for threefolds. |
| doi_str_mv | 10.1007/s00013-005-1445-4 |
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| title | Notes on very ample vector bundles on 3-folds |
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