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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Symmetric roots and admissible pairing
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by Robin de Jong PDF
Trans. Amer. Math. Soc. 363 (2011), 4263-4283 Request permission


Using the discriminant modular form and the Noether formula it is possible to write the admissible self-intersection of the relative dualising sheaf of a semistable hyperelliptic curve over a number field or function field as a sum, over all places, of a certain adelic invariant $\chi$. We provide a simple geometric interpretation for this invariant $\chi$, based on the arithmetic of symmetric roots. We propose the conjecture that the invariant $\chi$ coincides with the invariant $\varphi$ introduced in a recent paper by S.-W. Zhang. This conjecture is true in the genus $2$ case, and we obtain a new proof of the Bogomolov conjecture for curves of genus $2$ over number fields.
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Additional Information
  • Robin de Jong
  • Affiliation: Mathematical Institute, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
  • MR Author ID: 723243
  • Email:
  • Received by editor(s): June 29, 2009
  • Received by editor(s) in revised form: October 5, 2009
  • Published electronically: March 3, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 4263-4283
  • MSC (2010): Primary 11G20, 14G40
  • DOI:
  • MathSciNet review: 2792987