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

Title data

Kühn, Ulf ; Müller, Jan Steffen:
Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces.
In: Transactions of the American Mathematical Society. Vol. 369 (March 2017) Issue 3 . - pp. 1869-1894.
ISSN 1088-6850
DOI: https://doi.org/10.1090/tran/6787

Project information

Project title:
Project's official titleProject's id
No informationKU 2359/2-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We give an explicitly computable lower bound for the arithmetic self-intersection number ω² 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

Further data

Item Type: Article in a journal
Refereed: Yes
Subject classification: MSC (2010): Primary 14G40; Secondary 11G50, 11G30, 14H25
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 May 2017 09:50
Last Modified: 04 May 2017 09:50
URI: https://eref.uni-bayreuth.de/id/eprint/36942