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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On positivity of line bundles on Enriques surfaces


Author: Tomasz Szemberg
Journal: Trans. Amer. Math. Soc. 353 (2001), 4963-4972
MSC (2000): Primary 14J28; Secondary 14C20, 14E25
Published electronically: July 30, 2001
MathSciNet review: 1852089
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Abstract:

We study linear systems on Enriques surfaces. We prove rationality of Seshadri constants of ample line bundles on Enriques surfaces and provide lower bounds on these numbers. We show the nonexistence of $k$-very ample line bundles on Enriques surfaces of degree $4k+4$ for $k\geq 1$, thus answering an old question of Ballico and Sommese.


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Additional Information

Tomasz Szemberg
Affiliation: Institute of Mathematics, Reymonta 4, PL-30-059 Kraków, Poland
Address at time of publication: Department of Mathematics, University of Essen, FB6 Mathematik, D-45117 Essen, Germany
Email: szemberg@im.uj.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02788-X
PII: S 0002-9947(01)02788-X
Keywords: Enriques surfaces, Seshadri constants, generation of jets, $k$-very ampleness
Received by editor(s): June 1, 2000
Published electronically: July 30, 2001
Additional Notes: Partially supported by KBN grant 2 P03A 00816
Article copyright: © Copyright 2001 American Mathematical Society