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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A lower bound for sectional genera of ample and spanned vector bundles on algebraic surfaces


Authors: Antonio Lanteri and Francesco Russo
Journal: Proc. Amer. Math. Soc. 119 (1993), 1053-1059
MSC: Primary 14J60; Secondary 14C20
MathSciNet review: 1176482
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Abstract: Let $ E$ be an ample and spanned vector bundle of rank $ r$ over a complex projective surface $ S$. It is shown that the sectional genus $ g(S,\det E)$ is bounded from below by the number $ b = \max \{ q(S),2 - r\chi ({\mathcal{O}_S})\} $ and pairs $ (S,E)$ satisfying $ b \leqslant g(S,\det E) \leqslant b + 1$ are characterized.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1176482-3
PII: S 0002-9939(1993)1176482-3
Keywords: Surface (complex projective), vector bundle (ample), sectional genus, adjunction
Article copyright: © Copyright 1993 American Mathematical Society