Mathematics – Algebraic Geometry
Scientific paper
2009-06-11
Transactions of the AMS 363 (2011), 4263--4283
Mathematics
Algebraic Geometry
21 pages
Scientific paper
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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