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

 

Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves


Authors: Jun Lu and Sheng-Li Tan
Journal: Trans. Amer. Math. Soc. 365 (2013), 3373-3396
MSC (2010): Primary 14D06, 14C21, 14H10
Published electronically: December 3, 2012
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Abstract: In a family of curves, the Chern numbers of a singular fiber are the local contributions to the Chern numbers of the total space. We will give some inequalities between the Chern numbers of a singular fiber as well as their lower and upper bounds. We introduce the dual fiber of a singular fiber, and prove a duality theorem. As an application, we will classify singular fibers with large or small Chern numbers.


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Additional Information

Jun Lu
Affiliation: Department of Mathematics, East China Normal University, Dongchuan RD 500, Shanghai 200241, People’s Republic of China
Email: jlu@math.ecnu.edu.cn

Sheng-Li Tan
Affiliation: Department of Mathematics, East China Normal University, Dongchuan RD 500, Shanghai 200241, People’s Republic of China
Email: sltan@math.ecnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05625-X
PII: S 0002-9947(2012)05625-X
Keywords: Chern number, singular fiber, modular invariant, isotrivial, classification.
Received by editor(s): March 7, 2010
Received by editor(s) in revised form: March 19, 2011
Published electronically: December 3, 2012
Additional Notes: This work was supported by NSFC, the Science Foundations of the Education Ministry of China and the Foundation of Scientific Program of Shanghai.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.