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.
Carlson, Extensions of Mixed Hodge Structures, Journées de Géométrie Algébrique d'Angers 1979, Sijthoff e Nordhoff, Alphen an den Rijn, the Netherlands (1980), 107--127
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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.