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arXiv · 0906.2112

Symmetric roots and admissible pairing

Robin de Jong
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Abstract

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. We provide a simple geometric interpretation for this invariant, based on the arithmetic of symmetric roots. We propose the conjecture that the invariant introduced in this paper coincides with an invariant introduced in a recent paper by S.-W. Zhang.

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Robin de Jong. 2012-03-28. Symmetric roots and admissible pairing. https://arxiv.org/abs/0906.2112

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