Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces
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- by Ulf Kühn and J. Steffen Müller PDF
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Abstract:
We give an explicitly computable lower bound for the arithmetic self-intersection number $\overline {\omega }^2$ of the dualizing sheaf on a large class of arithmetic surfaces. If some technical conditions are satisfied, then this lower bound is positive. In particular, these technical conditions are always satisfied for minimal arithmetic surfaces with simple multiplicities and at least one reducible fiber, but we also use our techniques to obtain lower bounds for some arithmetic surfaces with non-reduced fibers.References
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Additional Information
- Ulf Kühn
- Affiliation: Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
- Email: kuehn@math.uni-hamburg.de
- J. Steffen Müller
- Affiliation: Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
- Address at time of publication: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany
- MR Author ID: 895560
- Email: jan.steffen.mueller@uni-oldenburg.de
- Received by editor(s): October 15, 2013
- Received by editor(s) in revised form: March 11, 2015
- Published electronically: June 2, 2016
- Additional Notes: The second author was supported by DFG grant KU 2359/2-1
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 1869-1894
- MSC (2010): Primary 14G40; Secondary 11G50, 11G30, 14H25
- DOI: https://doi.org/10.1090/tran/6787
- MathSciNet review: 3581222