Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces

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...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2017-03, Vol.369 (3), p.1869-1894
Main Authors: Ulf Kühn, J. Steffen Müller
Format: Article
Language:English
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6787