Mathematics – Algebraic Geometry
Scientific paper
2010-07-07
Mathematics
Algebraic Geometry
26 pages
Scientific paper
In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers for it when there is a place at which the closed subvariety is sufficiently degenerate in some sense. The key of the proof of our main theorem is the study of the minimal dimension of the components of a canonical measure on the tropicalization of the closed subvariety. Then we can apply the tropical version of the equidistribution theory by Gubler. This article includes an appendix by Walter Gubler. He shows there an equality which describes the minimal dimension of the components of a canonical measure with the dimension of the abelian part of the subvariety.
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