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Title: Graph invariants and the positivity of the height of the Gross-Schoen cycle for some curves
Authors: Yamaki, Kazuhiko  kyouindb  KAKEN_id  orcid (unconfirmed)
Author's alias: 山木, 壱彦
Issue Date: Jan-2010
Publisher: Springer-Verlag
Journal title: Manuscripta mathematica
Volume: 131
Issue: 1-2
Start page: 149
End page: 177
Abstract: Let X be a projective curve over a global field K. Gross and Schoen defined a modified diagonal cycle Δ on X3, and showed that the height $${langle Delta, Delta rangle}$$ is defined in general. Zhang recently proved a formula which describe $${langle Delta, Delta rangle}$$ in terms of the self pairing of the admissible dualizing sheaf and the invariants arising from the reduction graphs. In this note, we calculate explicitly those graph invariants for the reduction graphs of curves of genus 3 and examine the positivity of $${langle Delta, Delta rangle}$$ . We also calculate them for so-called hyperelliptic graphs. As an application, we find a characterization of hyperelliptic curves of genus 3 by the configuration of the reduction graphs and the property $${langle Delta, Delta rangle = 0}$$ .
Rights: The original publication is available at
この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。This is not the published version. Please cite only the published version.
DOI(Published Version): 10.1007/s00229-009-0305-0
Appears in Collections:Journal Articles

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