Estimates for Tamagawa numbers of diagonal cubic surfaces |
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Authors: | Andreas-Stephan Elsenhans Jörg Jahnel |
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Institution: | a Universität Bayreuth, Mathematisches Institut, Universitätsstraße 30, D-95447 Bayreuth, Germany b Fachbereich 6, Mathematik, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany |
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Abstract: | For diagonal cubic surfaces, we give an upper bound for E. Peyre's Tamagawa type number in terms of the coefficients of the defining equation. This bound shows that the reciprocal admits a fundamental finiteness property on the set of all diagonal cubic surfaces. As an application, we show that the infinite series of Tamagawa numbers related to the Fano cubic bundles considered by Batyrev and Tschinkel (1996) BT] are indeed convergent. |
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Keywords: | 11G35 11G50 11G40 14J20 14J26 |
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