For genus-three Ceresa cycles the limit height of the nilpotent orbit equals the Deligne splitting of the associated boundary biextension mixed Hodge structure once the parameter is fixed.
Griffiths, Infinitesimal variations of Hodge structure
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Genus three Ceresa cycles and limit of archimedean heights
For genus-three Ceresa cycles the limit height of the nilpotent orbit equals the Deligne splitting of the associated boundary biextension mixed Hodge structure once the parameter is fixed.