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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On vector bundles on $ 3$-folds with sectional genus $ 1$


Author: Edoardo Ballico
Journal: Trans. Amer. Math. Soc. 324 (1991), 135-147
MSC: Primary 14F05; Secondary 14J30
DOI: https://doi.org/10.1090/S0002-9947-1991-0986021-8
MathSciNet review: 986021
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Abstract: Here we give a classification (in characteristic zero) of pairs $ (V,E)$ with $ V$ being a smooth, connected, complete $ 3$-fold and $ E$ a rank-$ 2$ spanned ample vector bundle on $ V$ with sectional genus $ 1$. The proof uses the partial classification of Fano $ 3$-folds and Mori theory.


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DOI: https://doi.org/10.1090/S0002-9947-1991-0986021-8
Keywords: Fano $ 3$-fold, ample vector bundle, spanned bundle, sectional genus, adjunction map
Article copyright: © Copyright 1991 American Mathematical Society