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

 

Chern numbers of certain Lefschetz fibrations


Author: András K. Stipsicz
Journal: Proc. Amer. Math. Soc. 128 (2000), 1845-1851
MSC (1991): Primary 57R99, 57M12
Published electronically: October 18, 1999
Erratum: Proc. Amer. Math. Soc. 128 (2000), 2833-2834.
MathSciNet review: 1641113
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Abstract: We address the geography problem of relatively minimal Lefschetz fibrations over surfaces of nonzero genus and prove that if the fiber-genus of the fibration is positive, then $0\leq c_1^2\leq 5c_2$ (equivalently, $0\leq c_1^2 \leq 10 \chi _h $) holds for those symplectic 4-manifolds. A useful characterization of minimality of such symplectic 4-manifolds is also proved.


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Additional Information

András K. Stipsicz
Affiliation: Department of Analysis, ELTE TTK, 1088. Múzeum krt. 6-8., Budapest, Hungary
Address at time of publication: Department of Mathematics, University of California, Irvine, California 92697-3875
Email: stipsicz@cs.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05172-2
PII: S 0002-9939(99)05172-2
Keywords: 4-manifolds, Lefschetz fibrations, geography problem
Received by editor(s): June 29, 1998
Received by editor(s) in revised form: July 14, 1998
Published electronically: October 18, 1999
Additional Notes: Supported by the Magyary Zoltán Foundation and OTKA
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society