
Graph invariants and the positivity of the height of the GrossSchoen cycle for some curvesGraph invariants and the positivity of the height of the GrossSchoen cycle for some curvesAA00721187 
"/Yamaki, Kazuhiko/"Yamaki, Kazuhiko
131
(
12
)
, pp.149

177 , 201001
ISSN:00252611
NCID:AA00721187
Description
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 socalled 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 $${\langle \Delta, \Delta \rangle = 0}$$ .
FullText
http://repository.kulib.kyotou.ac.jp/dspace/bitstream/2433/128877/1/rev2graphinvmm.pdf